Question

the simple pendulum performs S. h. m of period 4 second how much time after crossing the mean position will the displacement of the bob be one third of the amplitude .​

Answer 1

Given :

Time  period (T) = 4sec

To find :

The time required for the particle to displace (1/3)rd of the amplitude

Solution :

• The displacement equation of the particle is given by x = Asinωt

• Initially the particle is at mean position so t=0 and x=0

• Let after time t it crosses (1/3)rd of its amplitude

          x = Asinωt

         (A/3) = Asinωt

         sinωt = 1/3

         ωt = sin⁻¹ (1/3)

• By applying the value of sin⁻¹ (1/3)

         ωt = 0.3398

         (2π/T)t = 0.3398

          t = 0.3398 × 4 / 2π

          t = 0.216 sec

The time required for the particle to displace (1/3)rd of the amplitude is 0.216s