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

In the rightmost arrangement (c), the two springs with spring constants k₁ and k₂ are connected in series. For springs in series, the equivalent spring constant k_ eq is given by: 1 k_ eq = 1 k₁ + 1 k₂ k_ eq = k₁ k₂ k₁ + k₂ The time period T of oscillation for a mass m attached to a spring system is: T = 2 m k_ eq Substituting the value of k_ eq : T = 2 m k₁ k₂ k₁ + k₂ = 2 m(k₁ + k₂) k₁ k₂