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 leftmost arrangement (a), both springs are connected between the same rigid support and the mass m . When the mass m is displaced by a distance x , both springs undergo the same extension or compression x . This indicates that the springs are connected in parallel. For springs in parallel, the equivalent spring constant k_ eq is the sum of the individual spring constants: k_ eq = k₁ + k₂ The time period of oscillation T for a spring-mass system is given by: T = 2 m k_ eq Substituting the value of k_ eq , we