Answer to Question #134087 in Classical Mechanics for Sridhar

Question

A simple harmonic oscillator of frequency 1Hz has a phase of 1 radian.By how much should the origin be shifted in time so as to make the phase of the oscillator vanish. (time in seconds (s)).
Ans: -1/2π

Answer 1

A phase of a simple harmonic oscillator is given by the following expression:

$$\varphi = \omega t$$

where $\omega = 2\pi f = 2\pi\cdot 1Hz = 2\pi$ is the angular frequency, $t$ is the time. If $\varphi = 1$, then

$$t = \dfrac{\varphi}{\omega} = \dfrac{1}{\omega} = \dfrac{1}{2\pi}$$

Thus, if we shift time by $-1/2\pi$, we get rid of the phase ($\varphi = 0$ ).

Answer. $t = \dfrac{1}{2\pi}$ s.