If a simple pendulum has significant amplitude (up to a factor of 1 / e of original) only in the period between t=0s to t= s , then may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with ' b ' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:

Step-by-step solution

As retardation = bv retarding force = mbv net restoring torque when angular displacement is is given by =- mg + mbv I =-m g + mbv where, I = m ^2 d ^2 dt ^2 = =- g + bv for small damping, the solution of the above differential equation will be = ₀ e ^ - bt 2 (w t+ ) angular amplitude will be = . e^ -b t 2 According to question, in time (average life-time), angular amplitude drops to 1 e value of its original value ( ) ₀ e = ₀ e ^ - 6 2 6 2 =1 = 2 b