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 circular motion of a particle with constant speed is

Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
$(a)$ The rotation of Earth about its axis.
$(b)$ Motion of an oscillating mercury column in a $U$-tube.
$(c)$ Motion of a ball bearing inside a smooth curved bowl,when released from a point slightly above the lowermost point.
$(d)$ General vibrations of a polyatomic molecule about its equilibrium position.

The motion of a particle as per $x = A \sin \omega t + B \cos \omega t$ is :-

The displacement equation of a simple harmonic oscillator is given by $y = A \sin \omega t - B \cos \omega t$. The amplitude of the oscillator will be

The displacement of a particle executing simple harmonic motion is given by
$y = A_{0} + A \sin \omega t + B \cos \omega t$
Then the amplitude of its oscillation is given by