Two identical springs are attached to a block of mass m. One spring is attached to the left side of the block, and the other to the right side. Both springs are identical and have spring constant k. When the block is displaced a distance x from equilibrium, what is the frequency of oscillation?

Core Concept

When the block is displaced a distance x, each spring exerts a force of magnitude kx. Since the springs are on opposite sides, their forces add up, resulting in a net restoring force of 2kx. This gives an effective spring constant of 2k. The frequency is given by f = (1/2π)√(k_eff/m) = (1/2π)√(2k/m).