# Homework Help: Simple Harmonic Motion with Rotational Inertia

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1. Aug 28, 2016

### Vanessa Le

1. The problem statement, all variables and given/known data
One end of a light spring with force constant k = 100 N/m is attached to a vertical wall. A light string is tied to the other end of the horizontal spring. the string changes from horizontal to vertical as it passes over a pulley of mass M in the shape of a solid disk of radius R = 2.00 cm. The
pulley is free to turn on a fixed, smooth axle. The vertical section of the string supports an object of mass m = 200 g. The string does not slip at its contact with the pulley. The object is pulled downward a small distance and released.

(a) What is the angular
frequency v of oscillation
of the object in terms of
the mass M?

(b)What
is the highest possible
value of the angular frequency
of oscillation of the object?

2. Relevant equations

w=(k/m)exp1/2

3. The attempt at a solution
I honestly do not know where to start... For a), wouldn't you simply use the w=(k/m)exp1/2 formula since the angular frequency only depends on the mass and the spring contsant?

Last edited: Aug 28, 2016
2. Aug 29, 2016

### ehild

Do you think that the mass of the pulley does not affect the angular frequency?

3. Aug 29, 2016

### Vanessa Le

In the problem, it stated that the pulley had a mass M with Radius = 2.00cm so I am assuming the mass of the pulley does matter, which lead me to thinking that the mass used in the w=(k/m)exp1/2 equation is in fact m = mass of object + mass of pulley.

I tried finding the mass of the pulley using the moment of inertia formula before realizing that I'd actually need the pulley mass for that too..

4. Aug 29, 2016

### ehild

The mass of the pulley does matter. It is M which can have different values. Solve the problem in terms of M and k. Write the acceleration of m with the forces acting on it and the angular acceleration of M with the angular momenta of the forces acting on it. What are those forces?

5. Aug 29, 2016

### Vanessa Le

What would I use to find the M mass of the pulley? I've tried moment of inertia and that doesn't work because you need the mass for I=MR^2.

6. Aug 29, 2016

### ehild

You can not find M. It is arbitrary. Find the frequency in terms of M.

7. Aug 29, 2016

### ehild

Draw the free-body diagram for m and M. What forces act on m, and at the rim of the disk? How is the acceleration of m related to these forces? How is the angular acceleration of the disk related to the torque of the forces acting at its rim?