If the frequency of a system undergoing simple harmonic motion doubles,by what factor does the maximum value of acceleration change?

Question

Quizplus · Accepted Answer

The maximum acceleration in simple harmonic motion is given by $a_{max} = \omega^2 x_{max}$, where $\omega$ is the angular frequency and $x_{max}$ is the maximum displacement. Since $\omega = 2\pi f$, doubling the frequency $f$ quadruples the square of the angular frequency $\omega^2$, thus quadrupling the maximum acceleration.

If the Frequency of a System Undergoing Simple Harmonic Motion 2\sqrt { 2 }2​

If the Frequency of a System Undergoing Simple Harmonic Motion $\sqrt { 2 }$