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The potential energy of a particle executing S.H.M. is $ 2.5\, J$, when its displacement is half of amplitude. The total energy of the particle be .... $J$
Abody performs simple harmonic oscillations along the straight line $ABCDE$ with $C$ as the midpoint of $AE.$ Its kinetic energies at $B$ and $D$ are each one fourth of its maximum value. If $AE = 2R,$ the distance between $B$ and $D$ is
A particle executing a simple harmonic motion of period $2\ s$ . When it is at its extreme displacement from its mean position, it receives an additional energy equal to what it had in its mean position. Due to this , in its subsequent motion,
A simple pendulum of length $ l$ has a brass bob attached at its lower end. Its period is $T$. If a steel bob of same size, having density $ x$ times that of brass, replaces the brass bob and its length is changed so that period becomes $2T$, then new length is
A particle of mass $m$ is moving along a trajectory given by
$x = x_0 + a\, cos\,\omega_1 t$
$y = y_0 + b\, sin\,\omega_2t$
The torque, acing on the particle about the origin, at $t = 0$ is
If the displacement of a particle executing $SHM $ is given by $y = 0.30\sin (220t + 0.64)$ in metre, then the frequency and maximum velocity of the particle is