Question

A machine, modeled as a simple spring-mass system, oscillates in simple harmonic motion. Its acceleration is measured to have an amplitude of 10,000 mm/s2 with a frequency of 8 Hz. Compute the maximum displacement the machine undergoes during this oscillation.

Answer 1

Answer:

3.96*10^-3 m

Explanation:

Given that

Amplitude, A = 10000 mm/s² = 10 m/s²

Frequency, f = 8 hz

the maximum acceleration of a simple harmonic motion is given as

|a|(max) = Aw², where

A = amplitude of the simple harmonic motion

w = angular frequency of the simple harmonic motion

Remember, w = 2πf, so

w = 2 * 3.142 * 8

w = 50.272 rad/s

Rearranging the formula, and making a the subject, we have

A = |a|(max) / w², so that

A = 10 / 50.272²

A = 10 / 2527.27

A = 0.00396 m

A = 3.96*10^-3 m