Physics - SHM Question with Solution | TestHub

The standard equation in SHM is

$x=a\cos (\omega t+\varphi )$...(i)

Where$a$is amplitude,$\omega$the angular velocity and ($\varphi$) the phase difference.

Also,$\omega =\frac{2\pi }{T } \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} T$is periodic time.

So, Eq. (i) becomes

$x=a\cos \left(\frac{2\pi t}{T}+\varphi \right)$...(ii)

Given, the equation is

$x=0.01\cos \left(\frac{2\pi t}{2}+\frac{\pi }{4}\right)$...(iii)

Comparing Eq. (ii) with Eq. (iii), we get

$\frac{2\pi t}{T}=\frac{2\pi t}{2}$

$\Rightarrow T=2 \mathrm{s}$

So, frequency$n=\frac{1}{T}=\frac{1}{2}=0.5 \mathrm{Hz}$