question_answer 35)

                  A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of \[60\text{ }cm/{{s}^{2}}\]. The period of oscillation is                 (a) \[\pi s\]                               (b) \[\frac{\pi }{2}s\]                 (c) \[2\pi \,s\]                   (d) \[\frac{\pi }{t}\,s\]

Answer:

                  (a) \[{{u}_{\max }}\,=\,\omega r\]                 and \[{{a}_{\max }}={{\omega }^{2}}r\]                 \[\therefore \] \[\omega =\,\frac{{{a}_{\max }}}{{{u}_{max}}}\,=\frac{60}{30}\,=2\]                 or \[T=\,\frac{2\pi }{\omega }=\,\pi s\]