The displacement of a body in a one–dimensional motion is represented by the equation : $x\left(t\right)=3\mathrm{sin\pi }t+4\mathrm{cos\pi }t$. Which one of the following is/are the correct statement (s):

Given, $x=3\mathrm{sin\pi }t+4\cos \omega t$

The general equation of SHM can be written as

$x=A\sin \left(\omega t+\varphi \right)$

or $x=A\sin \omega t\cos \varphi +A\cos \omega t\sin \varphi$

On comparing two equations, we get

$A\sin \varphi =4$ and $A\cos \varphi =3$

$\therefore A^2=25$ and $A=5$

So, $x=5\sin \left(\mathrm{\pi t}+\mathrm{\varphi }\right)$

Also $\omega =\mathrm{\pi }$

or $f=\frac{\omega }{\mathrm{\pi }}+\frac{\mathrm{\pi }}{2\mathrm{\pi }}=\frac{1}{2}Hz$