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LANS

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## Homework Statement

A mass M is attached to a spring with spring constant K. At the equilibrium point of the spring, the mass has a velocity of V.

M = 8.07 kg

K = 113 N/m

V_o = 0.638 m/s

How far does the mass travel until it stops? How long (in seconds) does it take for the mass to travel from the equilibrium point until it stops?

## Homework Equations

[tex]\frac{1}{2}MV_o^2 = \frac{1}{2}Kx^2[/tex] - equation 1

[tex] F(x) = kx[/tex] - spring force

[tex] V(x) = \sqrt{V_o^2 - \frac{Kx^2}{m}} [/tex] - from energy.

## The Attempt at a Solution

Using equation 1, I can solve part 1 easily. I plug in M,K,V to equation 1and solve for x, which gives me [tex]x = 0.1705m[/tex]

I have no idea how to solve part 2. I've tried using power, but that doesn't go anywhere meaningful.

[tex]P(x) = F(x)*V(x)[/tex]

Integrating for total power gives me

[tex] \frac{MV_o^2}{2t} = \int F(x)*V(x) [/tex]

Simplifying the integral:

[tex] \frac{MV_o^2}{2t} = \int \sqrt{K^2 x^2 V_o^2 - \frac{K^3 x^4}{m}} [/tex]

I've tried solving that for t, and it doesn't give me the right answer. I haven't thought of it yet, but I feel like there should be an easier solution to this problem. Any help is appreciated.