Q36 of 40 Page 103

A body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is 4cm below the point, where it was held in hand.

(a) What is the amplitude of oscillation?


(b) Find the frequency of oscillation?


a) When the box falls its potential energy changes and the change in potential energy = energy stored in the spring


∴


Where k=spring constant, x=displacement and m=mass of the box


-----(1)


Now at the equilibrium, let the amplitude of the spring be


∴ balancing the forces,



------(2)


Putting (1) in (2), we get,



Now



∴ the amplitude of oscillation = 2 cm


b) Time period of oscillation of the system is given as,





Now from equation 1, we have,




Putting the above in the frequency equation we get,


Hz


∴ the frequency is 3.52 Hz


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