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## Homework Statement

A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest:

a.) find the force between the bottom of the box and the block as a function of time;

b.) for what value of d does the block just begin to leave the bottom of the box at the top of the vertical osscilations?

## Homework Equations

F = -kx

## The Attempt at a Solution

I'm not exactly sure how to proceed with this.

I started with F

_{net}= mg + Mg -kx

I've rewritten it as [itex]\ddot{x} + \frac{k}{m + M}x = g[/itex]

where [itex]\ddot{x}[/itex] is the acceleration with respect to time

should I now just solve the differential equation? That should result in x as a function of time, and then take the second derivative of that and multiply it by the mass of the system?

the part b question seems pretty simple, though. Just take F

_{net}= mg + Mg -kx, set it equal to zero, replace x with d, and solve for d.