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

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.