A pendulum with the time period of 1 s is losing energy due to damping. At a certain time, its energy is 45 J . If after completing 15 oscillations its energy has become 15 J , then its damping constant (in s - 1 ) will be

Step-by-step solution

Energy of a damping oscillator is E = E 0 e -2 γ t at time t where γ = damping constant, E '   = E o e - 2 γ t ⇒ 15 = 45 e - 2 γ 15 ⇒ γ = 1 30 l n ⁡ ( 3 )