The motion of a particle executing $S.H.M.$ is given by $x = 0.01 \sin 100\pi (t + 0.05)$,where $x$ is in metres and $t$ is in seconds. The time period is ..... $sec$.

Which of the following expressions corresponds to simple harmonic motion along a straight line,where $x$ is the displacement and $a, b, c$ are positive constants?

Which of the following functions of time represent $(a)$ periodic and $(b)$ non-periodic motion? Give the period for each case of periodic motion $[\omega$ is any positive constant].
$(i)$ $\sin \omega t + \cos \omega t$
$(ii)$ $\sin \omega t + \cos 2\omega t + \sin 4\omega t$
$(iii)$ $e^{-\omega t}$
$(iv)$ $\log(\omega t)$

The displacement equation of a particle is $x = 3\sin 2t + 4\cos 2t$. The amplitude and maximum velocity will be respectively:

Study of which motion is required to understand many physical phenomena?

The displacement of a particle is represented by the equation $y = \sin^3 \omega t$. The motion is