The displacement $x$ (in metres) of a particle performing simple harmonic motion is related to time $t$ (in seconds) as $x = 0.05 \cos \left( 4 \pi t + \frac{\pi}{4} \right)$. The frequency of the motion will be ..... $Hz$.

The figure shows the circular motion of a particle. The radius of the circle is $B$. The particle starts at $t=0$ from the positive $y$-axis and moves clockwise. The simple harmonic motion of the $x$-projection of the radius vector of the rotating particle is given by:

The displacement of a particle varies according to the relation $x = 3 \sin 100t + 8 \cos^2 50t$. Which of the following is incorrect about this motion?

The displacement of a particle varies with time according to the relation $x = a \sin \omega t + b \cos \omega t$.

The figure shows the position-time graph of an object in $S.H.M.$ The correct equation representing this motion is ..........

The ratio of the maximum acceleration to the maximum velocity of a simple harmonic oscillator is