The displacement time equation of a particle executing $SHM$ is : $x = A \,sin\,(\omega t + \phi )$. At time $t = 0$ position of the particle is $x = A/2$ and it is moving along negative $x-$ direction. Then the angle $\phi $ can be
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Two particles execute $SHM$ of same amplitude of $20\, cm$ with same period along the same line about the same equilibrium position. The maximum distance between the two is $20\, cm.$ Their phase difference in radians is
A particle executing simple harmonic motion along $Y- $axis has its motion described by the equation $y = A\sin (\omega \,t) + B$. The amplitude of the simple harmonic motion is
Astone is swinging in a horizontal circle $0.8\, m$ in diameter at $30 \,rev / min.$ Adistant horizontal light beam causes a shadow of the stone to be formed on a nearly vertical wall. The amplitude and period of the simple harmonic motion for the shadow of the stone are
A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor, the velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$
A particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time $?$
$Assertion :$ In simple harmonic motion, the velocity is maximum when the acceleration is minimum.
$Reason :$ Displacement and velocity of $S.H.M.$ differ in phase by $\frac{\pi }{2}$
Two bodies performing $SHM$ have same amplitude and frequency. Their phases at a certain instant are as shown in the figure. The phase difference between them is
The angular velocity and the amplitude of a simple pendulum is $\omega $ and $a$ respectively. At a displacement $X$ from the mean position if its kinetic energy is $T$ and potential energy is $V$, then the ratio of $T$ to $V$ is
A point performs simple harmonic oscillation of period $T$ and the equation of motion is given by $x=Asin$$\left( {\omega t + \frac{\pi }{6}} \right)$. After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?