A mass $m$ is suspended from two massless springs connected in parallel. The force constants for the

Question

A mass $m$ is suspended from two massless springs connected in parallel. The force constants for the springs are $k_{1}$ and $k_{2}$. The time period of the suspended mass will be

Professor PC Thomas Classes · Answer

(a) : When two springs of spring constants $k_1$ and $k_2$ are connected in parallel, the equivalent spring constant is\  $k_{eq} = k_1 + k_2$. The time period of the oscillation is given by \ $T = 2\pi\sqrt{\frac{m}{k_{eq}}}$. Substituting $k_{eq}$, we get \ $T = 2\pi\sqrt{\frac{m}{k_1 + k_2}}$.