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A cylindrical block of density $\rho$ is partially immersed in a liquid of density $3\rho .$ The plane surface of the block remains parallel to the surface of the liquid. The height of the block is $60\, cm.$ The block performs $SHM$ when displaced from its mean position. [Use $ g = 9.8\, m/s^2$]
If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are
A pendulum suspended from the ceiling of a train oscillates with a time period $2$ $second$ , when the train is accelerating at $10\,ms^{-2}$. What will be its time period when the train retards at $10\,ms^{-2}$ ? .... $s$
A mass $m$ is suspended from a spring of force constant $k$ and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is
Two pendulums have time periods $T$ and $\frac{{5T}}{4}.$They start $S.H.M.$ at the same time from the mean position. What will be the phase difference between them after the bigger pendulum has complete one oscillation ..... $^o$
A block of mass $1 \,kg$ attached to a spring is made to oscillate with an initial amplitude of $12\, cm$. After $2\, minutes$ the amplitude decreases to $6\, cm$. Determine the value of the damping constant for this motion. (take In $2=0.693$ )
The equation of an $S.H.M.$ with amplitude $A$ and angular frequency $\omega$ in which all the distances are measured from one extreme position and time is taken to be zero at the other extreme position is ...
Spring of spring constant $1200\, Nm^{-1}$ is mounted on a smooth frictionless surface and attached to a block of mass $3\, kg$. Block is pulled $2\, cm$ to the right and released. The angular frequency of oscillation is .... $ rad/sec$
The acceleration $a$ of a particle undergoing $S.H.M.$ is shown in the figure. Which of the labelled points corresponds to the particle being at -$x_{max}$