Pendulums ~ period of oscillation

[brownie24]

Homework Statement

A pendulum is made of 2 disks, each of mass M and radius R separated by a massless rod. one of the disks is pivoted through its center by a small pin. The disks hang in the same plane and their centers are a distance L apart. Find the period for small oscillations.

Homework Equations

T = 2pi/omega

The Attempt at a Solution

I honestly haven't a clue how to start the problem. I am having trouble even visualizing it. Can anybody clarify what the question is?

 

[sArGe99]

Find the period of small oscillations...? Anything more is given?
I don't see any oscillations there..

 

[nlightner]

As a scientist, it is important to have a clear understanding of the question before attempting to solve it. From the given information, it appears that the question is asking for the period of oscillation for a pendulum made of two disks, each with a mass of M and radius of R, separated by a distance L and hung in the same plane. One disk is pivoted through its center by a small pin. The problem is asking for the period of small oscillations, which can be calculated using the equation T = 2pi/omega, where T is the period and omega is the angular frequency.

To solve this problem, we can start by considering the forces acting on the pendulum. The only forces acting on the pendulum are its weight and the tension in the rod. Since the disks are hung in the same plane, the weight of each disk can be considered to act at its center of mass. The tension in the rod acts along the length of the rod and can be considered to act at the point where the rod is attached to the pivot.

Next, we can use Newton's second law, F=ma, to write equations for the forces acting on each disk in the x and y directions. Since the pendulum is undergoing small oscillations, we can use the small angle approximation, sin(theta) = theta, to simplify our equations.

Once we have equations for the forces, we can use the equations of motion for simple harmonic motion, x(t) = A*cos(omega*t) and y(t) = A*sin(omega*t), where A is the amplitude, to find the value of omega. We can then use this value of omega to calculate the period of the pendulum using T = 2pi/omega.

It is important to note that the small angle approximation is only valid for small oscillations, so the period calculated using this method will only be accurate for small angles. For larger angles, a more complex analysis will be required.