Physics - SHM Question with Solution | TestHub

The resultant equation is

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

$\sum A_x=2+4\cos 30°+6\cos 60°=8.46$



And$\sum A_y=4\sin 30°+6\cos 30°=7.2$

$\therefore A=\sqrt{{\left(\sum A_x\right)}^2+{\left(\sum A_y\right)}^2}$

$= \sqrt{{\left(8.46\right)}^2+{\left(7.2\right)}^2}=11.25$

And$\tan \varphi =\frac{\sum A_y}{\sum A_x}=\frac{7.2}{8.46}=0.85$

$\Rightarrow \varphi ={\tan }^{-1}\left(0.85\right)=40.4°$

Thus, the displacement equation of combined motion is

$x=11.25\sin \left(\omega t+\varphi \right)$

Where,$\varphi =40.4°$