Observe the setup shown in the figure. The blocks are given slight displacements in opposite directions and then released, causing them to execute simple harmonic motion. Calculate the time period of the resulting motion.

Step-by-step solution

For a two-body oscillator system, the time period of oscillation is given by T = 2 k , where is the reduced mass of the system. The reduced mass for two masses m₁ and m₂ is = m₁ m₂ m₁ + m₂ . Given m₁ = m and m₂ = m , we get: = m m m + m = m^2 2m = m 2 Substituting the value of into the time period formula: T = 2 m/2 k = 2 m 2k