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 acceleration of the needle? A) 8.26 cm/s² B) 16.5 cm/s² C) 18.1 cm/s² D) 326 cm/s² E) 163 cm/s²

Question

Quizplus · Accepted Answer

The maximum acceleration of an object in simple harmonic motion can be found using the formula a_max = ω^2*A, where ω is the angular frequency (2πf) and A is the amplitude. 
In this case, ω = 2π(2.55 Hz) = 16.06 rad/s and A = 1.27 cm = 0.0127 m. 
Thus, a_max = (16.06 rad/s)^2 * 0.0127 m ≈ 3.26 m/s^2 = 326 cm/s^2. 
Therefore, the correct answer is D: 326 cm/s^2.

A Sewing Machine Needle Moves Up and Down in Simple