A particle is performing simple harmonic motion with amplitude A and angular velocity ${\omega }$. The ratio of maximum velocity to maximum acceleration is
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Two masses $M_{A}$ and $M_{B}$ are hung from two strings of length $l_{A}$ and $l_{B}$ respectively. They are executing SHM with frequency relation $f_{A}=2 f_{B}$, then relation
If the particle repeats its motion after a fixed time interval of $8 \,s$ then after how much time its maximum value of $PE$ will be attained after attaining its minimum value is ........... $s$
A particle is executing $SHM$ about $y=0$ along $y$-axis. Its position at an instant is given by $y=(7 \,m )$ sin( $\pi f)$. Its average velocity for a time interval $0$ to $0.5 \,s$ is ........... $m / s$
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 $10\,ms^{-2}$ ? ..... $\sec$
The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water, then the new time period is given by
A solid cylinder of density $\rho_0$, cross-section area $A$ and length $l$ floats in a liquid $\rho(> \rho_0)$ with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will be
The energy of a particle executing simple harmonic motion is given by $E = Ax^2 + Bv^2$, where $x$ is the displacement from mean position $x = 0$ and $v$ is the velocity of the particle at $x$ then choose the incorrect statement
The amplitude of a damped oscillator decreases to $0.9\,times$ its original magnitude in $5\,s.$ In another $10\,s$ it will decrease to $\alpha $ times its original magnitude, where $\alpha $ equals