$A$ particle is executing simple harmonic motion with time period $2 \ s$ and amplitude $1 \ cm$. If $D$ and $d$ are the total distance and displacement covered by the particle in $12.5 \ s$,then $\frac{D}{d}$ is:

If the displacement equation of a particle is represented by $y = A\sin PT + B\cos PT$,the particle executes

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

The function $x = A \sin^2 \omega t + B \cos^2 \omega t + C \sin \omega t \cos \omega t$ does not represent $SHM$ for which of the following conditions?

Linear simple harmonic motion is a projection of uniform circular motion along any one diameter of a circle. Is there any distinction between these two?

The equation of motion of a particle is given by $x = a \sin(50t + \frac{\pi}{3}) \text{ cm}$. The particle will come to rest at time $t_1$ and it will have zero acceleration at time $t_2$. The $t_1$ and $t_2$ respectively are . . . . . . .