Question

Two bodies, of equal masses M each, are suspended from two massless springs of spring constants k₁ and k₂ , respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibrations of the first body, to that of the second body, is

(1) k₁/k₂

(2) \(\sqrt{\frac{k_1}{k_2}}\)

(3) \(\frac{k_2}{k_1}\)

(4) \(\sqrt{\frac{k_2}{k_1}}\)

Answer 1

 (4) \(\sqrt{\frac{k_2}{k_1}}\)

For the two springs, we have

Let A₁ and A₂ be the amplitudes of their vibrations.

Now maximum velocity = velocity amplitude = A ω

We, therefore, have