An object attached to a spring is displaced by 4 cm and rele

An object attached to a spring is displaced by 4 cm and released to set it into oscillation with a period of time T. Later, the same object on the same spring is displaced by 8 cm and set into a oscillation again. What is the period of the second oscillation?

Solution

F = - kx ==> k = F/ x    k is spring constant, x displacemnent of the object attached to the spring

and time period T = 2*pi(sqrt(m/k)) = 2*pi (sqrt(m*x/F))

given x1 = 4 cm, x2 = 8 cm, m is same , T1, T2 are the timeperiods

if time for 4 cm displacement is T, then time period for 8 cm displacement would be greater than previous case that is 2 times the time period = 2T