Physics - SHM Question with Solution | TestHub

$x=4(\cos \pi t+\sin \pi t)=4\left[\sin \left(\frac{\pi }{2}-\pi t\right)\right]+\sin \pi t]=4\left[2\times \sin \left(\frac{\pi t-\frac{\pi }{2}-\pi t}{2}\right)\cos \left(\frac{\pi \mathrm{t}-\frac{\pi }{2}+\pi \mathrm{t}}{2}\right)\right]$ $=8\left[\sin \frac{\pi }{4}\cdot \cos \left(-\frac{\pi }{4}+\pi t\right)\right]$ $=\frac{8}{\sqrt{2}}\cdot \cos \left[\pi t-\frac{\pi }{4}\right]=4\sqrt{2}\cos \left[\pi t-\frac{\pi }{4}\right]$ Comparing it with standard equation $X=A\cos (wt-Kx)\Rightarrow A=4\sqrt{2}$