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 $29.8 \mathrm {~N} / \mathrm { m } \text {, }$ what is the potential energy stored in the mass-spring system when t = 1.42 s?
A)0.350 J
B)0.256 J
C)0.329 J
D)0.399 J

Question

Quizplus · Accepted Answer

The potential energy stored in the mass-spring system is given by:$$U = \frac{1}{2}kA^2\cos^2(\omega t)$$where k is the force constant, A is the maximum displacement, and $\omega$ is the angular frequency.At t = 1.42 s, we have:$$U = \frac{1}{2}(29.8 \mathrm {~N} / \mathrm { m } )(0.232 \mathrm {~m} )^2\cos^2(2.81 \mathrm {~rad/s} \times 1.42 \mathrm {~s}) = 0.350 \mathrm {~J}$$Therefore, the correct answer is A.

An Object Attached to an Ideal Spring Oscillates with an Angular