Two identical springs are attached to a block of mass m. One spring is attached to the left side and the other to the right side of the block. Both springs have the same spring constant k. The block is displaced a distance A from equilibrium and released. What is the angular frequency of oscillation?

Core Concept

When the block is displaced to the right, the left spring exerts a force F₁ = kx to the right, and the right spring exerts a force F₂ = kx to the left. The net restoring force is F = F₁ + F₂ = 2kx. Using F = -ma (negative because it's a restoring force), we have 2kx = -ma, or a = -(2k/m)x. This gives us the angular frequency ω = √(2k/m).