Question

What are the normal frequencies of oscillation for this mechanical system?

Answer 1

The mass of the cylindrical polley is M with radius R and is hung from the ceiling with two springs, one of them in one side (left and right, as you can see in the picture below). What are the normal frequencies of oscillations for this mechanical system in the small oscillations approximation?

Consider a general physical motion with 3 degrees of freedom, so the generalized coordinates are q≡(x,y,θ). Note that if you want to calculate the normal frequencies of oscillation the pendulum motion is irrelevant because it doesn't involve the springs.

Answer 2

$<marquee><b><u><i>Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.⭐️⭐️---------------✴️--------------⭐️⭐️$