To make a pendulum, a 410 g ball is attached to one end of a string that has a length of 1.8 m and negligible mass. (The other end of the string is fixed.) The ball is pulled to one side until the string makes an angle of 20° with the vertical; then (with the string taut) the ball is released from rest. Find (a) the speed of the ball when the string makes an angle of 14° with the vertical and (b) the maximum speed of the ball. (c) What is the angle between the string and the vertical when the speed of the ball is one-third its maximum value?
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.
To make a pendulum, a 410 g ball is attached to one end of a string that has a length of 1.8 m and negligible mass. (The other end of the string is fixed.) The ball is pulled to one side until the string makes an angle of 20° with the vertical; then (with the string taut) the ball is released from rest.
Find (a) the speed of the ball when the string makes an angle of 14° with the vertical and (b) the maximum speed of the ball.
(c) What is the angle between the string and the vertical when the speed of the ball is one-third its maximum value?
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