Question

Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant k₁ and k₂ respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of B is 

(a) k₁/k₂ 

(b) √(k₁/K₂) 

(c) k₂/k₁ 

(d) √(k₂/K₁).

Answer 1

(d) √(k₂/k₁)

EXPLANATION: 

The maximum velocity occurs at the mean position where the total energy is in the form of kinetic energy =½mv². Since the maximum velocities of both systems are equal, their total energy is also equal.         

 At the extreme position, the total energy is in the form of potential energy. These will also be equal. Let amplitude of A = A' and that of B = B'. Equating the total energy at extremes we get, ½k₁A'² = ½k₂B'² 

→A'²/B'² = k₂/k₁ 

→A'/B' = √(k₂/k₁) 

Hence the option (d).