3) A block of mass m hangs vertically at rest from a light cord of length 1. A bullet of mass with horizontal velocity v hits the block passes through and emerges with horizontal velocity, setting the block into small oscillation. a) What are the frequency and amplitude of the resulting simple harmonic motion of the block, assuming air drag can be ignored? b) Now assume that air drag cannot be ignored. For what value of the linear drag coefficient c will the motion be critically damped? c) Find the motion of the block as a function of time, assuming that the motion is critically amned
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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