If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum acceleration of the oscillator change?
A) 2
B) 4
C) 1
D) 1/2
E) 1/4

Question

Quizplus · Accepted Answer

The maximum acceleration of a simple harmonic oscillator is given by $a_{max} = \omega^2 A$, where $\omega$ is the angular frequency and $A$ is the amplitude of the oscillation.

When the frequency is doubled, the angular frequency $\omega$ becomes $2\omega$, and the amplitude $A$ remains the same. Therefore, the maximum acceleration is given by:

$a'_{max} = (2\omega)^2 A = 4\omega^2 A$

The ratio of the new maximum acceleration to the old maximum acceleration is:

$\frac{a'_{max}}{a_{max}} = \frac{4\omega^2 A}{\omega^2 A} = 4$

This means that the maximum acceleration is increased by a factor of 4 when the frequency is doubled. Therefore, the best choice is B.

If the Frequency of the Motion of a Simple Harmonic