The displacement of a particle varies according to the relation...

\left.x=4(\cos \pi t+\sin \pi t)=4\left[\sin\left(\frac{\pi}{2}-\pi t\right)\right]+\sin \pi t\right]=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 $X=A \cos (w t-K x) \quad \Rightarrow A=4 \sqrt{2}$