4. You hang a hula-hoop from a nail in the wall. The hula hoop has a radius R and mass M. [ a. Derive the equation for the moment of inertia of the hula hoop if it rotates around the nail. b. You tilt the hula hoop at a small angle and let it oscillate on the nail. This is animated on this homework's page on Canvas for you. Derive the equation for the period of the hula hoop. Y c. Sketch a graph of the period as a function of the radius of the hula hoop. D.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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