Two identical blocks are attached to two separate massless springs having spring constants k₁ and k₂ . They are made to oscillate vertically such that the maximum acceleration of both blocks is exactly the same. The ratio of the amplitude of the first block to the amplitude of the second block ( A₁ / A₂ ) is:

Step-by-step solution

Let the mass of each identical block be m . The maximum acceleration of a block executing simple harmonic motion is given by a_ = A ^2 , where A is the amplitude and is the angular frequency. For a spring-mass system, ^2 = k m . Thus, the maximum acceleration is a_ = A ( k m ) . Given that the maximum accelerations are equal for both blocks: A₁ ( k₁ m ) = A₂ ( k₂ m ) Since the masses are identical, m cancels out: A₁ k₁ = A₂ k₂ Rearranging this gives the ratio of their amplitudes: A₁ A₂ = k₂ k₁ Answer: k₂ k₁