For a periodic motion represented by the equation y = sin + cos the...

Given the equation of motion is

$y = sin \omegat + cos \omegat . . . \left(1\right)$

Simplify equation (1) to obtain the standard form:

$\begin{cases}y & = & \sqrt{2}\left(sin\omega tcos\dfrac{\pi}{4} + cos\omega tsin\dfrac{\pi}{4}\right) \\ & = & \sqrt{2}\sin \left(\omegat + \dfrac{\pi}{4}\right) . . . \left(2\right)\end{cases}$

Comparing equation (2) with standard equation of SHM $y = Asin\left(\omegat + ϕ\right)$, we get amplitude of the given oscillation as $\sqrt{2}$.