## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 1)

A mass of $$25$$ kg is attached to a certain spring such that $$48$$ Newtons of force is required to compress the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$9.2$$ seconds.

The IVP is given by

$25x''+16x=0 \hspace{3em} x(0)=-3, x'(0)=0$

The position after $$9.2$$ seconds is approximately $$1.42$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 2)

A mass of $$25$$ kg is attached to a certain spring such that $$18$$ Newtons of force is required to compress the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$3.5$$ seconds.

The IVP is given by

$25x''+9x=0 \hspace{3em} x(0)=-2, x'(0)=0$

The position after $$3.5$$ seconds is approximately $$1.01$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 3)

A mass of $$9$$ kg is attached to a certain spring such that $$125$$ Newtons of force is required to compress the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$7.9$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=-5, x'(0)=0$

The position after $$7.9$$ seconds is approximately $$4.12$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 4)

A mass of $$16$$ kg is attached to a certain spring such that $$18$$ Newtons of force is required to stretch the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$8.8$$ seconds.

The IVP is given by

$16x''+9x=0 \hspace{3em} x(0)=2, x'(0)=0$

The position after $$8.8$$ seconds is approximately $$1.90$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 5)

A mass of $$4$$ kg is attached to a certain spring such that $$32$$ Newtons of force is required to compress the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$5.5$$ seconds.

The IVP is given by

$4x''+16x=0 \hspace{3em} x(0)=-2, x'(0)=0$

The position after $$5.5$$ seconds is approximately $$0.00885$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 6)

A mass of $$25$$ kg is attached to a certain spring such that $$27$$ Newtons of force is required to stretch the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$4.6$$ seconds.

The IVP is given by

$25x''+9x=0 \hspace{3em} x(0)=3, x'(0)=0$

The position after $$4.6$$ seconds is approximately $$2.78$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 7)

A mass of $$25$$ kg is attached to a certain spring such that $$80$$ Newtons of force is required to stretch the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$5.9$$ seconds.

The IVP is given by

$25x''+16x=0 \hspace{3em} x(0)=5, x'(0)=0$

The position after $$5.9$$ seconds is approximately $$0.0391$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 8)

A mass of $$25$$ kg is attached to a certain spring such that $$32$$ Newtons of force is required to stretch the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$9.4$$ seconds.

The IVP is given by

$25x''+16x=0 \hspace{3em} x(0)=2, x'(0)=0$

The position after $$9.4$$ seconds is approximately $$0.656$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 9)

A mass of $$16$$ kg is attached to a certain spring such that $$36$$ Newtons of force is required to compress the mass $$4$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$2.9$$ seconds.

The IVP is given by

$16x''+9x=0 \hspace{3em} x(0)=-4, x'(0)=0$

The position after $$2.9$$ seconds is approximately $$2.27$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 10)

A mass of $$25$$ kg is attached to a certain spring such that $$27$$ Newtons of force is required to compress the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$9.1$$ seconds.

The IVP is given by

$25x''+9x=0 \hspace{3em} x(0)=-3, x'(0)=0$

The position after $$9.1$$ seconds is approximately $$2.04$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 11)

A mass of $$9$$ kg is attached to a certain spring such that $$8$$ Newtons of force is required to compress the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$2.4$$ seconds.

The IVP is given by

$9x''+4x=0 \hspace{3em} x(0)=-2, x'(0)=0$

The position after $$2.4$$ seconds is approximately $$0.0583$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 12)

A mass of $$9$$ kg is attached to a certain spring such that $$48$$ Newtons of force is required to stretch the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$4.5$$ seconds.

The IVP is given by

$9x''+16x=0 \hspace{3em} x(0)=3, x'(0)=0$

The position after $$4.5$$ seconds is approximately $$2.88$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 13)

A mass of $$4$$ kg is attached to a certain spring such that $$50$$ Newtons of force is required to stretch the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$2.2$$ seconds.

The IVP is given by

$4x''+25x=0 \hspace{3em} x(0)=2, x'(0)=0$

The position after $$2.2$$ seconds is approximately $$1.42$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 14)

A mass of $$4$$ kg is attached to a certain spring such that $$50$$ Newtons of force is required to compress the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$6.2$$ seconds.

The IVP is given by

$4x''+25x=0 \hspace{3em} x(0)=-2, x'(0)=0$

The position after $$6.2$$ seconds is approximately $$1.96$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 15)

A mass of $$16$$ kg is attached to a certain spring such that $$16$$ Newtons of force is required to stretch the mass $$4$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$2.6$$ seconds.

The IVP is given by

$16x''+4x=0 \hspace{3em} x(0)=4, x'(0)=0$

The position after $$2.6$$ seconds is approximately $$1.07$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 16)

A mass of $$9$$ kg is attached to a certain spring such that $$32$$ Newtons of force is required to stretch the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$1.0$$ seconds.

The IVP is given by

$9x''+16x=0 \hspace{3em} x(0)=2, x'(0)=0$

The position after $$1.0$$ seconds is approximately $$0.470$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 17)

A mass of $$9$$ kg is attached to a certain spring such that $$75$$ Newtons of force is required to stretch the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$3.1$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=3, x'(0)=0$

The position after $$3.1$$ seconds is approximately $$1.32$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 18)

A mass of $$25$$ kg is attached to a certain spring such that $$36$$ Newtons of force is required to compress the mass $$4$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$9.8$$ seconds.

The IVP is given by

$25x''+9x=0 \hspace{3em} x(0)=-4, x'(0)=0$

The position after $$9.8$$ seconds is approximately $$3.68$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 19)

A mass of $$9$$ kg is attached to a certain spring such that $$125$$ Newtons of force is required to stretch the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$3.3$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=5, x'(0)=0$

The position after $$3.3$$ seconds is approximately $$3.54$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 20)

A mass of $$9$$ kg is attached to a certain spring such that $$64$$ Newtons of force is required to stretch the mass $$4$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$8.2$$ seconds.

The IVP is given by

$9x''+16x=0 \hspace{3em} x(0)=4, x'(0)=0$

The position after $$8.2$$ seconds is approximately $$0.248$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 21)

A mass of $$4$$ kg is attached to a certain spring such that $$80$$ Newtons of force is required to compress the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$6.8$$ seconds.

The IVP is given by

$4x''+16x=0 \hspace{3em} x(0)=-5, x'(0)=0$

The position after $$6.8$$ seconds is approximately $$2.56$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 22)

A mass of $$9$$ kg is attached to a certain spring such that $$8$$ Newtons of force is required to stretch the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$9.7$$ seconds.

The IVP is given by

$9x''+4x=0 \hspace{3em} x(0)=2, x'(0)=0$

The position after $$9.7$$ seconds is approximately $$1.97$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 23)

A mass of $$4$$ kg is attached to a certain spring such that $$45$$ Newtons of force is required to compress the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$6.1$$ seconds.

The IVP is given by

$4x''+9x=0 \hspace{3em} x(0)=-5, x'(0)=0$

The position after $$6.1$$ seconds is approximately $$4.81$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 24)

A mass of $$9$$ kg is attached to a certain spring such that $$75$$ Newtons of force is required to stretch the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$8.4$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=3, x'(0)=0$

The position after $$8.4$$ seconds is approximately $$0.410$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 25)

A mass of $$9$$ kg is attached to a certain spring such that $$125$$ Newtons of force is required to stretch the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$4.3$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=5, x'(0)=0$

The position after $$4.3$$ seconds is approximately $$3.17$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 26)

A mass of $$25$$ kg is attached to a certain spring such that $$32$$ Newtons of force is required to stretch the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$5.9$$ seconds.

The IVP is given by

$25x''+16x=0 \hspace{3em} x(0)=2, x'(0)=0$

The position after $$5.9$$ seconds is approximately $$0.0157$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 27)

A mass of $$4$$ kg is attached to a certain spring such that $$125$$ Newtons of force is required to compress the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$1.6$$ seconds.

The IVP is given by

$4x''+25x=0 \hspace{3em} x(0)=-5, x'(0)=0$

The position after $$1.6$$ seconds is approximately $$3.27$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 28)

A mass of $$9$$ kg is attached to a certain spring such that $$125$$ Newtons of force is required to compress the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$2.7$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=-5, x'(0)=0$

The position after $$2.7$$ seconds is approximately $$1.05$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 29)

A mass of $$25$$ kg is attached to a certain spring such that $$48$$ Newtons of force is required to compress the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$6.0$$ seconds.

The IVP is given by

$25x''+16x=0 \hspace{3em} x(0)=-3, x'(0)=0$

The position after $$6.0$$ seconds is approximately $$0.262$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 30)

A mass of $$9$$ kg is attached to a certain spring such that $$50$$ Newtons of force is required to stretch the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$7.1$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=2, x'(0)=0$

The position after $$7.1$$ seconds is approximately $$1.49$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 31)

A mass of $$4$$ kg is attached to a certain spring such that $$64$$ Newtons of force is required to compress the mass $$4$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$8.8$$ seconds.

The IVP is given by

$4x''+16x=0 \hspace{3em} x(0)=-4, x'(0)=0$

The position after $$8.8$$ seconds is approximately $$1.26$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 32)

A mass of $$16$$ kg is attached to a certain spring such that $$125$$ Newtons of force is required to compress the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$9.5$$ seconds.

The IVP is given by

$16x''+25x=0 \hspace{3em} x(0)=-5, x'(0)=0$

The position after $$9.5$$ seconds is approximately $$3.85$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 33)

A mass of $$4$$ kg is attached to a certain spring such that $$45$$ Newtons of force is required to stretch the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$1.4$$ seconds.

The IVP is given by

$4x''+9x=0 \hspace{3em} x(0)=5, x'(0)=0$

The position after $$1.4$$ seconds is approximately $$2.52$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 34)

A mass of $$16$$ kg is attached to a certain spring such that $$75$$ Newtons of force is required to compress the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$8.7$$ seconds.

The IVP is given by

$16x''+25x=0 \hspace{3em} x(0)=-3, x'(0)=0$

The position after $$8.7$$ seconds is approximately $$0.361$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 35)

A mass of $$9$$ kg is attached to a certain spring such that $$100$$ Newtons of force is required to stretch the mass $$4$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$7.3$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=4, x'(0)=0$

The position after $$7.3$$ seconds is approximately $$3.69$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 36)

A mass of $$25$$ kg is attached to a certain spring such that $$36$$ Newtons of force is required to compress the mass $$4$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$4.0$$ seconds.

The IVP is given by

$25x''+9x=0 \hspace{3em} x(0)=-4, x'(0)=0$

The position after $$4.0$$ seconds is approximately $$2.95$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 37)

A mass of $$25$$ kg is attached to a certain spring such that $$80$$ Newtons of force is required to compress the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$4.3$$ seconds.

The IVP is given by

$25x''+16x=0 \hspace{3em} x(0)=-5, x'(0)=0$

The position after $$4.3$$ seconds is approximately $$4.78$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 38)

A mass of $$4$$ kg is attached to a certain spring such that $$32$$ Newtons of force is required to stretch the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$1.3$$ seconds.

The IVP is given by

$4x''+16x=0 \hspace{3em} x(0)=2, x'(0)=0$

The position after $$1.3$$ seconds is approximately $$1.71$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 39)

A mass of $$25$$ kg is attached to a certain spring such that $$16$$ Newtons of force is required to compress the mass $$4$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$1.2$$ seconds.

The IVP is given by

$25x''+4x=0 \hspace{3em} x(0)=-4, x'(0)=0$

The position after $$1.2$$ seconds is approximately $$3.55$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 40)

A mass of $$9$$ kg is attached to a certain spring such that $$8$$ Newtons of force is required to stretch the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$6.4$$ seconds.

The IVP is given by

$9x''+4x=0 \hspace{3em} x(0)=2, x'(0)=0$

The position after $$6.4$$ seconds is approximately $$0.862$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 41)

A mass of $$9$$ kg is attached to a certain spring such that $$125$$ Newtons of force is required to compress the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$5.3$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=-5, x'(0)=0$

The position after $$5.3$$ seconds is approximately $$4.15$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 42)

A mass of $$9$$ kg is attached to a certain spring such that $$125$$ Newtons of force is required to stretch the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$4.2$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=5, x'(0)=0$

The position after $$4.2$$ seconds is approximately $$3.77$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 43)

A mass of $$4$$ kg is attached to a certain spring such that $$48$$ Newtons of force is required to stretch the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$5.8$$ seconds.

The IVP is given by

$4x''+16x=0 \hspace{3em} x(0)=3, x'(0)=0$

The position after $$5.8$$ seconds is approximately $$1.70$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 44)

A mass of $$4$$ kg is attached to a certain spring such that $$48$$ Newtons of force is required to stretch the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$1.3$$ seconds.

The IVP is given by

$4x''+16x=0 \hspace{3em} x(0)=3, x'(0)=0$

The position after $$1.3$$ seconds is approximately $$2.57$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 45)

A mass of $$25$$ kg is attached to a certain spring such that $$32$$ Newtons of force is required to stretch the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$2.2$$ seconds.

The IVP is given by

$25x''+16x=0 \hspace{3em} x(0)=2, x'(0)=0$

The position after $$2.2$$ seconds is approximately $$0.376$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 46)

A mass of $$9$$ kg is attached to a certain spring such that $$75$$ Newtons of force is required to compress the mass $$3$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$9.2$$ seconds.

The IVP is given by

$9x''+25x=0 \hspace{3em} x(0)=-3, x'(0)=0$

The position after $$9.2$$ seconds is approximately $$2.79$$ meters outward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 47)

A mass of $$25$$ kg is attached to a certain spring such that $$18$$ Newtons of force is required to compress the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$1.6$$ seconds.

The IVP is given by

$25x''+9x=0 \hspace{3em} x(0)=-2, x'(0)=0$

The position after $$1.6$$ seconds is approximately $$1.15$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 48)

A mass of $$4$$ kg is attached to a certain spring such that $$64$$ Newtons of force is required to stretch the mass $$4$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$7.6$$ seconds.

The IVP is given by

$4x''+16x=0 \hspace{3em} x(0)=4, x'(0)=0$

The position after $$7.6$$ seconds is approximately $$3.50$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 49)

A mass of $$9$$ kg is attached to a certain spring such that $$8$$ Newtons of force is required to compress the mass $$2$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$2.0$$ seconds.

The IVP is given by

$9x''+4x=0 \hspace{3em} x(0)=-2, x'(0)=0$

The position after $$2.0$$ seconds is approximately $$0.470$$ meters inward.

## C7m - Mass-spring systems. Model and analyze mechanical oscillators with a second-order IVP. (ver. 50)

A mass of $$16$$ kg is attached to a certain spring such that $$20$$ Newtons of force is required to stretch the mass $$5$$ meters from its natural position.

Write an initial value problem (IVP) modeling the position of this mass when released from rest. Then solve this IVP to compute the mass's position after $$4.6$$ seconds.

$16x''+4x=0 \hspace{3em} x(0)=5, x'(0)=0$
The position after $$4.6$$ seconds is approximately $$3.33$$ meters inward.