Frequency of Small Oscillations

[Piglet1024]

1. A uniform coin with radius R is pivoted at a point that is a distance d from its center. The coin is free to swing back and forth in the vertical plane defined by the plane of the coin. For what value of d is the frequency of small oscillations largest?



2. V(x)$$\equiv$$potential energy; V(x)$$\approx$$$$\frac{1}{2}$$V"(x$$_{o}$$)(x-x$$_{o}$$)$$^{2}$$ ; omega is equal to the square root of V"(x)/m



3. I have no idea what to do. My textbook is vague and my notes from lecture are not sufficient. I don't want a solution, just a push in the right direction

 

[kuruman]

Treat this as a physical pendulum. Begin by finding the moment of inertia about the pivot.

 

[kerimek]

.Hi there,

I am happy to provide some guidance on this topic. First, let's break down the information provided in the question.

1. We have a uniform coin with a radius R that is pivoted at a distance d from its center. This means that the coin is able to swing back and forth in a vertical plane.

2. The potential energy of the coin is represented by V(x), and we are given an approximation for V(x). We can see that the frequency of oscillations is related to the second derivative of V(x) (represented by V"(x)) and the mass of the coin (represented by m).

3. It seems like you are unsure of where to start with this problem. One approach could be to use the equation given for the potential energy and determine the second derivative (V"(x)) and the mass (m) of the coin. From there, you can plug these values into the equation for the frequency of small oscillations (omega) and see how it is affected by the distance d.

Another approach could be to think about the physical factors that affect the frequency of small oscillations, such as the mass and the force of gravity. How might these factors be affected by the distance d?

I encourage you to review your textbook and notes for more information on oscillations and potential energy. You can also try looking up similar problems online or consulting with your instructor for further clarification.

Best of luck!