Determine the time period of the mass m , assuming the string, spring, and pulley shown in the figure are light.

Step-by-step solution

Let the equilibrium extension of the spring be x₀ . At equilibrium, the tension in the string balances the weight of the mass m . T₀ = mg The tension is also equal to the spring force. T₀ = kx₀ kx₀ = mg When the mass m is displaced downwards by a distance x , the string pulls the spring upwards by the same distance x . The new extension of the spring becomes x₀ + x . The new tension in the string is T = k(x₀ + x) . The net restoring force acting on the mass m in the downward direction is: F = mg - T F = mg - k(x₀ +