A pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_1$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is $K_2$ then
JEE MAIN 2019, Medium
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Maximum kinetic energy at lowest point $B$ is given by
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A simple pendulum of length $1\, m$ is oscillating with an angular frequency $10\, rad/s$. The support of the pendulum starts oscillating up and down with a small angular frequency of $1\, rad/s$ and an amplitude of $10^{-2}\, m$. The relative change in the angular frequency of the pendulum is best given by
A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force $F\sin \omega t$. If the amplitude of the particle is maximum for $\omega = {\omega _1}$ and the energy of the particle is maximum for $\omega = {\omega _2}$, then (where ${\omega _0}$ natural frequency of oscillation of particle)
Five identical springs are used in the following three configurations. The time periods of vertical oscillations in configurations (i), (ii) and (iii) are in the ratio
The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of $\pi $ results in the displacement of the particle along
If the displacement of a particle executing $SHM $ is given by $y = 0.30\sin (220t + 0.64)$ in metre, then the frequency and maximum velocity of the particle is
A cylindrical plastic bottle of negligible mass of filled with $310\, ml$ of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $\omega $. If the radius of the bottle is $2.5\, cm$ then $\omega $ is close to ..... $rad\, s^{-1}$ (density of water $= 10^3\, kg/m^3$)
A particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time $?$
A particle executes simple harmonic motion (amplitude $= A$) between $x = - A$ and $x = + A$. The time taken for it to go from $0$ to $A/2$ is ${T_1}$ and to go from $A/2$ to $A$ is ${T_2}$. Then