A vertical mass spring system executes simple harmonic oscillations with a period of $2\,s$. A quantity of this system which exhibits simple harmonic variation with a period of $1\, sec$ is
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Two bodies $M$ and $N $ of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude $M$ to that of $N$ is
The periodic time of a body executing simple harmonic motion is $3\, sec$. After how much interval from time $t = 0$, its displacement will be half of its amplitude ..... $\sec$
The angular frequency of a spring block system is $\omega _0.$ This system is suspended from the ceiling of an elevator moving downwards with a constant speed $v_0.$ The block is at rest relative to the elevator. Lift is suddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement :
The graphs in figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graphs best represents the relationship obtained when $y$ is The total energy of the system
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
A block of mass m, attached to a spring of spring constant $k$, oscillates on a smooth horizontal table. The other end of the spring is fixed to a wall. The block has a speed $v$ when the spring is at its natural length. Before coming to an instantaneous rest, if the block moves a distance $x$ from the mean position, then
Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two motions is $.....(degree)$
A uniform rod of length $2.0 \,m$ is suspended through an end and is set into oscillation with small amplitude under gravity. The time period of oscillation is approximately .... $\sec$