Explain When two Springs are Connected in Parallel

When two Springs are Connected in Parallel:

Two springs of spring factors k₁ and k₂ are suspended from a rigid support as shown in Figure. A load m is attached to the combination.

Let the load be pulled downwards through a distance y from its equilibrium position. The increase in length is y for both the springs but their restoring forces are different.

If F₁ and F₂ are the restoring forces

F₁ = – k₁y,        F₂ = – k₂y

Total restoring force = (F₁ + F₂) = – (k₁ + k₂) y

So, time period of the body is given by;

T = 2π √[m/( k₁ + k₂)]

If, k₁ = k₂ = k; then,

T = 2π √(m/2k)

And frequency n = 1/2π √(2k/m)