(a) What is the maximum extension of the spring in the two cases?

(b) If the mass in Fig. (a) and the two masses in Fig. (b) is released, what is the period of oscillation in each case?

Solution:

(a) The maximum extension of the spring in fig (a) is .

The response force operating on the other mass is equal to the force acting on each mass. The two masses behave as if they are fixed in relation to each other.

Therefore,

where,

is the spring constant

(b) The restoring force on the mass in figure (a) is , where is the spring extension.

For the mass of the block, force can be calculated as

So,

Here, angular frequency of oscillation will be

Time period of oscillation will be

The system’s centre is 0 in Figure (b), and there are two springs. Each spring is in length and is linked to two masses.

Therefore

here is the extension of the spring.