# Vertical simple harmonic motion concept

1. Nov 20, 2009

### caljuice

1. The problem statement, all variables and given/known data
A 0.12-kg block is suspended from a spring. When a small stone of mass 30 g is placed on the block, the spring stretches an additional 5 cm. With the stone on the block, the spring oscillates with an amplitude of 12 cm. What is the net force of the stone when it is at a point of maximum upward displacement

3. The attempt at a solution

The answer is Fnet= mass of pebble x gravity. The solution says this is the case because the spring isnt moving.

But shouldn't Fnet = force of gravity + force of spring? Since at maximum compression, the spring will exert a down acceleration. Just because it's not moving doesn't have to mean it isn't causing acceleration right? And when I look at the position graph and the acceleration graph of horizontal simple harmonics, the greatest magnitude of acceleration of a spring is when the spring is at maximum compression or stretch- the amplitude. If there's acceleration then there must be force? Or is this different because this is vertical? Thanks.

2. Nov 21, 2009

### ehild

You are right, zero velocity do not mean zero acceleration. Assuming the pebble attached to the block during the oscillation, its acceleration has the highest magnitude at maximum displacement.
The solution might be correct if the box did not push the pebble at the top. The pebble is not fixed, so the block can only push it. But for that, an acceleration higher than g would be needed. You can calculate the angular frequency of oscillation, assuming that the block and pebble move together, and from that you get the maximum downward acceleration as amplitude times w2. It is less than g!

ehild