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. How long does it take it to travel 11.43 cm?
A) 3.53 s
B) 0.882 s
C) 1.13 s
D) 1.76 s
E) 2.65 s

Question

Quizplus · Accepted Answer

The time for one complete cycle is the period, T = 1/frequency = 1/2.55 Hz = 0.392 s. The needle travels 4 times the amplitude in one cycle (up and down twice), so it travels 4 * 1.27 cm = 5.08 cm per cycle. To travel 11.43 cm, it takes 11.43 cm / 5.08 cm per cycle = 2.25 cycles. Therefore, the time taken is 2.25 cycles * 0.392 s/cycle = 0.882 s.

A Sewing Machine Needle Moves Up and Down in Simple