Question 3: A careful student says that he can predict the frequency of spring-mass system though he knows that how far the spring stretches when the mass is hung from it. How he justifies himself?

ANSWER

The student is justified in his claim of prediction the frequency of spring-mass system if he knows the stretching (elongation) produced in the spring when the mass is attached to it. His argument may go like this.

Suppose the elongation produced in the string when the mass is attached to it = x
Now, we know that F = kx     …       (1) .
As the frequency is

The force applied by the mass is its weight. Therefore, put F = mg in equation (1)

Put in equation (2)

As he knows the stretching ‘x’ in the spring and ‘π’ and ‘g’ are already known constants. Therefore, he can find the frequency of the system.