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A disc of mass $m$ and radius $R$ is attached to celling with the help of ropes of length $l$. Find the time period of small oscillation of disc in the plane of disc.
A simple pendulum of frequency $f$ has a metal bob. If bob is charged negatively and is allowed to oscillate with large positive charged plate under it, frequency will be
A particle is excuting a simple harmonic motion. Its maximum acceleration is $\alpha $ and maximum velocity is $\beta $. Then its frequency of vibration will be
A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, $x_1(t)=A \sin \omega t $ and $ x_2(t)=A \sin \left(\omega t+\frac{2 \pi}{3}\right)$. Adding a third sinusoidal displacement $x_3(t)=B \sin (\omega t+\phi)$ brings the mass to a complete rest. The values of $B$ and $\phi$ are
A $LCR$ circuit behaves like a damped harmonic oscillator. Comparing it with a physical springmass damped oscillator having damping constant $\mathrm{b}$, the correct equivalence would be:
A particle at the end of a spring executes simple harmonic motion with a period ${t_1}$, while the corresponding period for another spring is ${t_2}$. If the period of oscillation with the two springs in series is $T$, then
A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 \mathrm{~m}$, then the time period of small oscillations will be ____ $s$. $\left[\right.$ take $\left.\mathrm{g}=\pi^2 \mathrm{~ms}^{-2}\right]$
A block of mass $m$ is at rest on an another block of same mass as shown in figure. Lower block is attached to the spring, then the maximum amplitude of motion so that both the block will remain in contact is