When a oscillator completes 100 oscillations its amplitude reduces to 1 3 of the initial value. What will be its amplitude when it completes 200 oscillations?

Step-by-step solution

Let a₀ be the initial amplitude and b be the damping constant The used formula is a=a₀ e^ -b t In Ist case : t=100 T and a= a₀ 3 a₀ 3 =a₀ e^ -b(100 T) aligned & e^ -b 100 T = 1 3 & In 2nd case : t=200 T & a=a₀ e^ -200 b T & a=a₀ (e^ -100 b T )^2 & a=a₀ ( 1 3 )^2 & a= a₀ 9 aligned