Question

A mass m is attached to two springs as shown in figure. The spring constants of two springs are $K_1$ and $K_2$. For the frictionless surface, the time period of oscillation of mass m is

Answer 1

$T = 2\pi \sqrt{\frac{m}{K_1 + K_2}}$\n

Answer 2

The two springs are connected in parallel to the mass. For springs in parallel, the effective spring constant is the sum of the individual spring constants: $K_{eff} = K_1 + K_2$. The time period of oscillation for a mass m attached to a spring with effective spring constant $K_{eff}$ is given by the formula $T = 2\pi \sqrt{\frac{m}{K_{eff}}}$. Substituting the effective spring constant, we get $T = 2\pi \sqrt{\frac{m}{K_1 + K_2}}$.