Two simple harmonic motions are represented by equations $y_1 = 4 \sin(10t + \phi)$ and $y_2 = 5 \cos(10t)$. What is the phase difference between their velocities?

The displacement of a body executing $SHM$ is given by $x = A \sin (2\pi t + \pi /3).$ The first time from $t = 0$ when the velocity is maximum is .... $\sec$

$A$ particle performing linear $S.H.M.$ of amplitude $0.1 \,m$ has displacement $0.02 \,m$ and acceleration $0.5 \,m/s^2$. The maximum velocity of the particle in $m/s$ is

$A$ particle of mass $5 \ g$ performs simple harmonic motion with an amplitude of $10 \ cm$. Its maximum velocity is $100 \ cm/s$. At what distance from the mean position will its velocity be $50 \ cm/s$?

$A$ body is executing simple harmonic motion with an angular frequency $2\,rad/s$. The velocity of the body at $20\,mm$ displacement,when the amplitude of motion is $60\,mm$,is ...... $mm/s$.

The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of $1.0 \; m$. If the piston moves with simple harmonic motion with an angular frequency of $200 \; rad/min$,what is its maximum speed in $m/min$?