3 Resonance and Quality Factor The quality factor Q of an oscillating system is a measure of how well the system stores energy: where an is the natural frequency of the oscillator, y is the damping coefficient, T is the period of oscillation, and r is the decay time. (a) A child on a swing stops kicking her legs. She swings back and forth about 20 times before the swing effectively comes to a stop. Assume that the final amplitude of the swing is about 2 percent of its initial value: i.e., the final amplitude is e- times the initial amplitude. What is Q for the swing? (b) The Mossbauer effect is a very sharp resonance of atomic nuclei in solids that involves emission or absorption of a gamma ray. The resonant frequency of this transition is about 1.5 x 1021 Hz. The full width at half maximum (FWHM) of the resonance is about 1.5 x 10'" Hz. What is Q for this transition?
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.
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