A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm.If the mass of the object is 0.20 kg,what is the spring constant?
A)40 N/m
B)87 N/m
C)126 N/m
D)160 N/m

Question

Quizplus · Accepted Answer

The formula for the frequency of simple harmonic motion is:
f = 1/(2π) √(k/m)
where f is the frequency, k is the spring constant, and m is the mass.

We have f = 4.0 Hz, and m = 0.20 kg. Also, the amplitude A = 8.0 cm which can be converted to meters by dividing by 1000.

4.0 = 1/(2π) √(k/0.20)
16π^2 = k/0.20
k = 16π^2 x 0.20
k = 126 N/m

Therefore, the spring constant is 126 N/m. Answer choice C is correct.

A Mass on a Spring Vibrates in Simple Harmonic Motion