Question

An object attached to an ideal spring oscillates with an angular frequency of 2.81 rad/s. the object has a maximum displacement at t = 0.00 s of 0.232 m. if the force constant (spring constant is 29.8 n/m, what is the potential energy stored in the mass-spring system when t = 1.42 s?

Answer 1

Ω = 2.81
A = 0.232
k = 29.8

x = A cos(ωt + Ф)

at t = 0:
x = A = A cos(ωt + Ф) = A cos(Ф)
Ф = 0

at t = 1.42, with Ф = 0:
x = A cos(ωt) 

U = 1/2 k x² = 1/2 k [A cos(ωt)]²