Let the mass m be displaced by a small distance x to the right as shown in Figure. Due to it, the spring on the left hand side gets stretched by length x and the spring on the right hand side gets compressed by length x. The forces acting on the mass due to springs are
F1 = – kx towards left hand side
F2 = – kx towards left hand side
Therefore, total restoring force on mass m is
F = F1 + F2 = – kx + (– kx) = –2 kx ...(i)
Here –ve sign shows that force F is directed towards the equilibrium position O and F x. Therefore, if the mass m is left free, it will execute linear SHM.
Comparing (i) with the relation, F = – kx, we have Spring factor, K = 2 k
Here, interia factor = mass of the block = m