14.44 . CALC The balance wheel of a watch vibrates with an angular amplitude 0, angular frequency w, and phase angle + = 0. (a) Find expressions for the angular velocity de/dt and angular acceleration d0/dt? as functions of time. (b) Find the bal- ance wheel's angular velocity and angular acceleration when its angular displacement is 0, and when its angular displacement is 0/2 and 0 is decreasing. (Hint: Sketch a graph of 0 versus t.)
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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Book reference : university physics with modern physics 13th edition
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