An observant fan at a baseball game notices that the radio commentators have lowered a microphone from their booth to just a few inches above the ground. The microphone is used to pick up sounds from the field and from the fans. The fan also notices that the microphone is slowly swinging back and forth like a simple pendulum. Using her digital watch, she finds that 12 complete oscillations take 60.0s. How high above the field is the radio booth? (Assume the microphone and its cord can be treated as a simple pendulum.)
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.
An observant fan at a baseball game notices that the radio commentators have lowered a microphone from their booth to just a few inches above the ground. The microphone is used to pick up sounds from the field and from the fans. The fan also notices that the microphone is slowly swinging back and forth like a simple pendulum. Using her digital watch, she finds that 12 complete oscillations take 60.0s.
How high above the field is the radio booth? (Assume the microphone and its cord can be treated as a simple pendulum.)
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