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## Homework Statement

A 0.5 kg mass is attached to a string that is 20 cm tall and anchored to a pole. There is an angle between the string and the pole.

1) What is the force of gravity on the mass in terms of the angle?

2) If the mass is pulled slightly to an angle of 5 degrees and if sin(theta) is congruent to theta, find an equation and its solution that best fits the case when at time = 0 the mass is held at 5 degrees. (If you are stuck, please consider the following two questions: a) What is the moment of inertia of the mass on the string in terms of mass and string length L? b) What is the expression for the angular acceleration I(omega) in terms of mass and string length L and d(theta)/dt when one notes that d(theta)/dt = omega?)

3) Will the mass oscillate if the mass is released after being pulled to 5 degrees?

4) If it oscillates, what is the angular frequency if the mass is 0.2 kg?

5) If it oscillates, does doubling the mass change the frequency, and if so how?

6) If it oscillates, does doubling the length of the string change the frequency, and if so how?

## Homework Equations

omega = 2(pi)(frequency)

## The Attempt at a Solution

1) The only one I could really answer. Fsin(theta), which is equal to mgsin(theta).

2) I don't know. I absolutely don't understand this. My teacher would only give me the answer (900 m) and told me I have to figure out the solution on my own. And I don't get it.

3) I think it could. It can go into simple harmonic motion, although it is eventually slowed by friction and air resistance. Plus, I don't think my teacher would have asked questions 4-6 if this wasn't yes.

4) omega

5)

6)

I am having an unbelievably hard time with this. This is an intro to physics class, and I can't believe my teacher would seriously give this when she did not go over the subject. I've been self-teaching, and I'm still not sure I got the topic 100%. I seriously need someone to guide me through this. Any and all help is appreciated!