A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. What is the maximum speed of the needle?
A) 3.18 cm/s
B) 4.51 cm/s
C) 20.3 cm/s
D) 10.1 cm/s
E) 6.36 cm/s

Question

Quizplus · Accepted Answer

The equation for the velocity of a mass undergoing simple harmonic motion is:

v = Aωcos(ωt)

Where A is the amplitude, ω is the angular frequency (ω = 2πf), and t is time.

At the maximum displacement (i.e. at the amplitude), the velocity is zero. Therefore, the maximum velocity occurs at the equilibrium position (where the displacement is zero).

Thus, when t = 0, we have:

v = Aωcos(0) = Aω

Plugging in the values given, we get:

v = (1.27 cm)(2π(2.55 Hz)) ≈ 20.3 cm/s

Therefore, the maximum speed of the needle is 20.3 cm/s, which corresponds to answer choice C.

A Sewing Machine Needle Moves Up and Down in Simple