Two bodies A and B , having the same mass, are hung from separate massless springs with spring constants k₁ and k₂ , respectively. If these bodies undergo vertical oscillation with identical maximum velocities, what is the ratio of the amplitude of A to the amplitude of B ?

Step-by-step solution

The maximum velocity of a body in simple harmonic motion is given by v_ max = A , where A is the amplitude and is the angular frequency. For a spring-mass system, the angular frequency is = k m . Given that the maximum velocities of both bodies are identical, v_ max, A = v_ max, B . Therefore, A_A _A = A_B _B . Substituting the expressions for , we get A_A k₁ m = A_B k₂ m . Since the masses are the same, this simplifies to A_A k₁ = A_B k₂ . Rearranging to find the ratio of the amplitudes, we obtain A_A A_B = k₂ k₁