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.
A simple pendulum is set into motion at two different times with different initial conditions. The first time: the bob is in its equilibrium position and is given an initial velocity +4 m/s. The maximum height reached by the bob is h1,max and the period of motion is T1. The second time: the bob is in its equilibrium position and is given an initial velocity +2 m/s. The maximum height reached by the bob is h2,max and the period of motion is T2. Assume that the motion is simple harmonic, which of the following is true?
a) h2,max = 4h1,max and T2=T1
b)h2,max=9h1,max and T2=T1
c)h2,max=4h1,max and T2=2T1
d)h2,max=h1,max/4 and T2=T1
e)h2,max=9h1,max and T2=3T1
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