Question

In the arrangement shown in figure, pulleys are light and springs are ideal. k₁, k₂, k₃ and k₄ are force constants of the springs. Calculate period of small vertical oscillations of block of mass m.

Answer 1

When the mass m is displaced from its mean position by a distance x, let F be the restoring (extra tension) force produced in the string. By this extra tension further elongation in the springs are 

Here negative sign shows the restoring nature of force.