Two blocks of masses m and 4m are attached to two identical massless springs. They are made to oscillate on a frictionless horizontal surface. If the maximum velocities of the two blocks are equal, the ratio of the amplitude of the lighter block to the amplitude of the heavier block is

Step-by-step solution

Let the spring constant of both identical springs be k . The maximum velocity of a block in simple harmonic motion is given by v_ = A , where the angular frequency is = k m . Given that the maximum velocities are equal ( v_ , 1 = v_ , 2 ): A₁ k m₁ = A₂ k m₂ Rearranging for the ratio of amplitudes: A₁ A₂ = m₁ m₂ Substituting the given masses m₁ = m and m₂ = 4m : A₁ A₂ = m 4m = 1 4 = 1 2 Answer: 1:2