The time period of oscillation of a spring is 1.57s when a mass of 100 gm is suspended from its lower end. Calculate (i) the force constant of the spring (ii) the K.E. of the mass when its displacement'is equal to the amplitude.

The time period of oscillation of a spring is 1.57s when a mass of 100

1.	The time period of oscillation of a spring is 1.57s when a mass of 100 gm is suspended from its lower end. Calculate (i) the force constant of the spring (ii) the K.E. of the mass when its displacement'is equal to the amplitude.
Answer» Solution :`m = 100gm=0.100 kg , T = 1.57 s, K = ? ` `T = 2pi SQRT(m/k)` `T^2 = 4pi^2(m)/k` `k = (4pi^2m)/(T^2)` `=(4xx(3.14)^2xx0.100)/((1.57)^2)=1.6 NM^(-1)` When the displacement is equal to the amplitude the velocity of the body is zero and hence K.E. is zero.