1 \(A=x_{0} \omega^{2}, \delta=3 \pi / 4\)
2 \(A=x_{0}, \delta=-\pi / 4\)
3 \(A=x_{0} \omega^{2}, \delta=\pi / 4\)
4 \(A=x_{0} \omega^{2}, \delta=-\pi / 4\)
Explanation:
Here,
\(x=x_{0} \cos (\omega t-\pi / 4)\)
\(\therefore\) Velocity, \(v=\dfrac{d x}{d t}=-x_{0} \omega \sin \left(\omega t-\dfrac{\pi}{4}\right)\)
Acceleration, \(a=\dfrac{d v}{d t}=-x_{0} \omega^{2} \cos \left(\omega t-\dfrac{\pi}{4}\right)\)
\( = {x_0}{\omega ^2}\cos \left[ {\pi + \left( {\omega t - \frac{\pi }{4}} \right)} \right]\)
\( = {x_0}{\omega ^2}\cos \left( {\omega t + \frac{{3\pi }}{4}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
Acceleration, \(a=A \cos (\omega t+\delta)\)
Comparing the two equations, we get
\(A=x_{0} \omega^{2} \text { and } \delta=\dfrac{3 \pi}{4} .\)
