A student was supplied with a stop watch, two metre rules and a simple pendulum suspended from a ceiling and was asked to measure the height of the ceiling indirectly. He set the pendulum swinging through a small angle and measured the period of oscillation for different lengths of the pendulum. Since he was unable to measure the length of the pendulum directly, he measured the height of the centre of the pendulum bob above the floor. He obtained the results tabulated below.
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.
C. Why was h measured to the center of the bob?
d. Why was the completed number of oscillation chosen to be large?
e. Can you see any advantage in measuring the height of the ceiling in this way?
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