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what do you know about mean lifetime of an un-damped harmonic oscillator and damped harmonic oscillator

what do you know about mean lifetime of an un-damped harmonic oscillator and damped harmonic oscillator
 

Grade:12th pass

1 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
2 years ago
Damping causesoscillatory systems to dissipate energy to their surroundings. Frictional losses are quite common in mechanicalsystemsand result in damped simple harmonic motion. For example, when a child stops pumping a swing, the amplitude of the oscillations gradually decay toward zero. The same thing happens to a mass that hangs from an oscillatingspring. It is quite common for the amplitude of such oscillations to exhibit a behavior that is negative exponential over time, as shown in Figure 1. The graphindicates that if we take the amplitude at time t=0 to be 1, then the amplitude at time t=1 is 1/e (0.37) of its value at time t=0. In other words, the amplitude decrease by 37% of its current value every 1 unit of time. For example, at time t=2, the amplitude would be 0.37 x 0.37 = 0.137 arbitrary units. At time t=3, the amplitude would be 0.137 x 0.37 = 0.05 arbitrary units. The time intervalτduring which the amplitude drops to 1/e of its initial value is known as mean lifetime of the oscillation.

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