$A$ particle performs $SHM$ on the $x-$axis with a time period of $0.5 \, s,$ such that its velocity is zero at $x = -3 \, cm$ and at $x = 9 \, cm$. It was located at $x = 0$ and moving in the negative $x-$direction at $t = 0$. The equation of $SHM$ of the particle is:

The figure depicts four $x-t$ plots for the linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?

$A$ particle moves in $S.H.M.$ such that its acceleration is $a = -px$,where '$x$' is the displacement of the particle from the equilibrium position and '$p$' is a constant. The period of oscillation is

One end of a rod of length $L$ is fixed to a point on the circumference of a wheel of radius $R$. The other end is sliding freely along a straight channel passing through the centre of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity $\omega$ about $O$. Taking $T = \frac{2 \pi}{\omega}$,the motion of the rod is

$A$ particle is oscillating according to the equation $X = 7 \cos(0.5 \pi t)$,where $t$ is in seconds. The particle moves from the position of equilibrium to maximum displacement in time ..... $s$.

The motion of a particle executing simple harmonic motion is described by the displacement function,$x(t) = A \cos (\omega t + \phi)$. If the initial $(t = 0)$ position of the particle is $1 \; cm$ and its initial velocity is $\omega \; cm/s$,what are its amplitude and initial phase angle? The angular frequency of the particle is $\pi \; s^{-1}$. If instead of the cosine function,we choose the sine function to describe the $SHM$: $x = B \sin (\omega t + \alpha)$,what are the amplitude and initial phase of the particle with the above initial conditions?