Determine the time period of the oscillation of mass m and the equivalent spring constant of the pair of springs for the rightmost arrangement shown in the figure.

Step-by-step solution

For the middle arrangement (b), let the mass m be displaced by a small distance x to the right from its equilibrium position. The left spring gets stretched by x , so it exerts a restoring force F₁ = k₁ x towards the left. The right spring gets compressed by x , so it exerts a restoring force F₂ = k₂ x towards the left. The net restoring force acting on the mass is F = -(F₁ + F₂) = -(k₁ x + k₂ x) = -(k₁ + k₂)x . Comparing this with F = -k_ eq x , we get the equivalent spring constant k_ eq = k₁ + k₂ . The time peri