Question

A simple harmonic motion is represented by $$x = 10\sin (20t + 0.5)$$.
Write down its amplitude, angular frequency, frequency, time period and initial phase if displacement is measured in metres and time in second.

Answer 1

$$x = 10\sin (20t + 0.5) .....(1)$$
Equation of SHM
$$x = A \sin (\omega t + \phi) ..... (2)$$
$$A = amplitude$$
$$\omega =$$ angular frequency
$$\phi =$$ initial phase
Comparing coefficients of $$(1)$$ and $$(2)$$
$$A = 10\ m$$
$$\omega = 20\ rad\ s^{-1}$$
$$\phi = 0.5\ rad$$
$$\omega = 2\pi f$$
$$f = \dfrac {\omega}{2\pi} = \dfrac {20}{2\times 3.14} = 3.18\ Hz$$
$$T = \dfrac {2\pi}{\omega} = 2\pi \dfrac {2\times 3.14}{20} = 0.314\ s$$.