A body of mass 2 kg suspended from a vertical spring undergoes simple harmonic motion with a period of 4 s . If the oscillations are halted and the body hangs in equilibrium, determine the potential energy stored in the spring.

Step-by-step solution

The time period of the spring-mass system is given by T = 2 m k . Substituting the given values: 4 = 2 2 k Squaring both sides: 16 = 4 ^2 ( 2 k ) k = 8 ^2 16 = ^2 2 N/m Taking ^2 10 , we get k = 5 N/m . At equilibrium, the spring force balances the weight of the body: kx = mg x = mg k = 2 10 5 = 4 m The potential energy stored in the spring at equilibrium is: U = 1 2 kx^2 U = 1 2 5 (4)^2 = 40 J