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#### Fascheue

## Homework Statement

A particle of mass m is subject to a force F(x) = kx, with k > 0. The initial position is x0, and the initial speed is zero. Find x(t).

## Homework Equations

F(x) = kx

F = ma

## The Attempt at a Solution

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F = kx

ma = kx

d^2x/dt^2 = kx/m

dx/dt = (kx^2)/(2m)

x^-2dx = (k/2m)dt

-x^-1 = kt/2m + c

-x^-1 = kt/2m + x0

x(t) = -2m/kt - 1/x0

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