Question

The function of time representing a simple harmonic motion with a period of $\pi/\omega$ is

Answer 1

The function of time representing a simple harmonic motion with a period of $\pi/\omega$ is of the general form $y(t) = A \sin(2\omega t + \phi)$ or $y(t) = A \cos(2\omega t + \phi)$.

Answer 2

The period $T$ of a simple harmonic motion (SHM) is related to its angular frequency $\Omega$ by the formula $T = \frac{2\pi}{\Omega}$. Given $T = \frac{\pi}{\omega}$, we equate the two: $\frac{2\pi}{\Omega} = \frac{\pi}{\omega}$. Solving for $\Omega$, we get $\Omega = 2\omega$. Thus, the SHM function must have an angular frequency of $2\omega$. The general form is $y(t) = A \sin(2\omega t + \phi)$ or $y(t) = A \cos(2\omega t + \phi)$.