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.
In the arrangement shown below, (screenshot attached) an object can be hung from a string (with linear mass density
that passes over a light pulley. The string is connected to a vibrator (of constant frequency f), and the length of the string between point P and the pulley is
When the mass m of the object is either 9.0 kg or 16.0 kg, standing waves are observed; no standing waves are observed with any mass between these values, however.
(a)What is the frequency of the vibrator (in Hz)?
(b)What is the largest object mass (in kg) for which standing waves could be observed?
(c) What would the linear mass density of the string have to be (in kg/m) if 16.0 kg is the largest mass for which standing waves are observed?
(d) For what values of m (in kg) would standing waves with the next four higher numbers of nodes be observed in this case? (m1 =?, m2=, m3=, m4=, m5=)
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