Question

Two particles A B of equal masses are suspended from two massless springs of spring constant K1 and K2 respectively.If the acceleration during oscillations are equal,what is the ratio of the displacements of A and B?

Answer 1

Given a₁ =a₂ and m₁ = m₂
we know
$$\begin{gathered} a=-{\omega }^{2}x \\ let{x}_{1}and{x}_{2}betheirdisplacementthen \\ \frac{x_1}{x_2}=\frac{{{\omega }_2}^2}{{{\omega }_1}^2}=\frac{k_2}{k_1}as{\omega }^2=\frac{k}{m} \end{gathered}$$