# Homework Help: Simple Harmonic Motion conceptual question

1. Feb 18, 2012

### getty102

1. The problem statement, all variables and given/known data
Answer the following questions for a mass that is hanging on a spring and oscillating up and down with simple harmonic motion. Note: the oscillation is small enough that the spring stays stretched beyond its rest length the entire time.

Answers available: Top, Equilibrium, Bottom, Top and Bottom, and Nowhere
I'm not sure where I'm going wrong.

1. Where in the motion is the speed a maximum? Equilibrium
2. Where in the motion is the magnitude of the force from the spring on the mass zero? Top
3. Where in the motion is the acceleration zero? Equilibrium
4. Where in the motion is the magnitude of the acceleration a maximum? Top and Bottom
5. Where in the motion is the speed zero? Top and Bottom
6. Where in the motion is the magnitude of the force from the spring on the mass a maximum? Bottom
7. Where in the motion is the magnitude of the net force on the mass a maximum? Top
8. Where in the motion is the magnitude of the net force on the mass zero? Equilibrium

There are two separate yes/no questions

1.When the object is at half its amplitude from equilibrium, is its speed half its maximum speed? Yes
2. When the object is at half its amplitude from equilibrium, is the magnitude of its acceleration at half its maximum value? Yes

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: Feb 18, 2012
2. Feb 18, 2012

### vela

Staff Emeritus

3. Feb 18, 2012

### cepheid

Staff Emeritus

The part of your post that I've highlighted in bold is important. The spring is always stretched at all times during the motion. Therefore, the restoring force from the spring is always upwards and non-zero. That's why your response to 2 is wrong.

Your response to 7 contradicts your response to 4. The latter is correct -- the acceleration is the same in magnitude at both ends of the oscillation, and it is at a maximum. This means, just by Newton's second law, that the net force has the same magnitude at both ends, and is at a maximum.

But you don't have to just take my word for it. Write an expression down for the net force on the mass. It will depend partly on the spring force, which in turn will depend on the vertical position, y, of the spring. (Note: y is measured from the "rest" length of the spring). You can easily compute y0, the equilibrium position. You can also compute the force at positions y0 + A and y0 - A (i.e. at the two endpoints of the motion), where A is the amplitude of the oscillation.