What is the total energy of a 15-kg mass attached to a spring oscillating horizontally with an amplitude of 20 cm and an angular frequency of 32 rad/s?
A)250 J
B)125 J
C)307 J
D)439 J
E)541 J

Question

Quizplus · Accepted Answer

The total energy of a simple harmonic oscillator is given by the formula:

E = 1/2 kA^2

where k is the spring constant, A is the amplitude of the oscillation.

We can find the spring constant k using the angular frequency:

k = mω^2

where m is the mass attached to the spring, and ω is the angular frequency.

Therefore, k = 15 kg x (32 rad/s)^2 = 15360 N/m.

Now we can substitute the values of k and A into the formula for energy:

E = 1/2 kA^2 = 1/2 x 15360 N/m x (0.2 m)^2 = 307.2 J.

Rounding this value to three significant figures, we get:

E = 307 J answer choice is (C).

What Is the Total Energy of a 15-Kg Mass Attached