There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum is
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A particle undergoing simple harmonic motion has time dependent displacement given by $x(t)\, = \,A\,\sin \,\frac{{\pi t}}{{90}}$. The ratio of kinetic to potential energy $o$ the particle at $t=210\,s$ will be
A particle is performing simple harmonic motion
$(i)$ its velocity-displacement graph is parabolic in nature
$(ii)$ its velocity-time graph is sinusoidal in nature
$(iii)$ its velocity-acceleration graph is elliptical in nature
Correct answer is
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 book is resting on a shelf that is undergoing vertical simple harmonic oscillations with an amplitude of $2.5 \,cm$. What is the minimum frequency of oscillation of the shelf for .......... $Hz$ the book will lose contact with the shelf? (Assume that, $g=10 \,ms ^{-2}$ )
A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\theta $ with the vertical
A particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then, its time period of vibration will be