The amplitudes of a damped harmonic oscillator after 2 and 4 seconds are A₁ and A₂ respectively. If the initial amplitude of the oscillator is A ₀ , then

Step-by-step solution

In damping harmonic oscillator, amplitude aligned & A=A₀ e^ -b t & A₁=A₀ e^ -b 2 A₁ A₀ =e^ -2 b aligned And aligned & A₂=A₀ e^ -b 4 A₂ A₀ =e^ -4 b = (e^ -2 b )^2= ( A₁ A₀ )^2 & or, A₂ A₀ = ( A₁ A₀ )^2= A₁^2 A₀^2 or, A₂ A₁^2 = 1 A₀ A₁= A₀ A₂ aligned