Question

If x=-cost+3sint, what is the amplitude and phase of the oscillation?

Answer 1

\[-\cos t + 3 \sin t = -r (\cos t \cos \theta - \sin t \sin \theta) \] say, then we can solve for amplitude \[r\] and phase \[ \theta \]
\[r = \sqrt{10}, \theta = \arctan{3}\]
\[x = -r\sqrt{10} \cos (t + \arctan 3)\]

Answer 2

\[-\cos t + 3 \sin t = -r (\cos t \cos \theta - \sin t \sin \theta) \] say, then we can solve for amplitude \[r\] and phase \[ \theta \]
\[r = \sqrt{10}, \theta = \arctan{3}\]
\[x = -r\sqrt{10} \cos (t + \arctan 3)\]