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## Homework Statement

A 3 kg object is moving along the x-axis where U(x) = 4x

^{2}. At x = -.5, v = +2. Find the object's position and KE as functions of time. Assume x = 0 at time t = 0. All forces acting on the object are conservative.

## Homework Equations

ME = U + K

K = (1/2)mv

^{2}

F = dU/dx

F = ma

## The Attempt at a Solution

Using initial conditions, ME = 4.

F = dU/dx = 8x

F = ma

8x = (3)d

^{2}x/dt

^{2}

This is where I got stuck. I was attempting to solve for x(t), find v(t), then use that to find K(t). Assuming everything else is correct, how do you solve a second order differential equation like this? Otherwise, please correct me.