Explanation

(a) The standard equation in SHM is
$x = a\cos{(\omega t + \varnothing)}$ …(i)
Where $a$ is amplitude, $\omega$ the angular velocity and ($\varnothing$) the phase difference.
Also, $\omega = \frac{2\pi}{T\ }\ where\ T$ is periodic time.
So, Eq. (i) becomes
$x = a\cos\left( \frac{2\pi t}{T} + \varnothing \right)$ …(ii)
Given, 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
$\frac{2\pi t}{T} = \frac{2\pi t}{2}$
$\Rightarrow \ \ \ \ \ \ \ \ \ T = 2$s
So, frequency $n = \frac{1}{T} = \frac{1}{2} = 0.5$ Hz