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A simple pendulum with a bob of mass $‘m’$ oscillates from $A$ to $ C$ and back to $A$ such that $PB$ is $H.$ If the acceleration due to gravity is $‘g’$, then the velocity of the bob as it passes through $B$ is
A particle is doing simple harmonic motion of amplitude $0.06 \mathrm{~m}$ and time period $3.14 \mathrm{~s}$. The maximum velocity of the particle is. . . . .. . $\mathrm{cm} / \mathrm{s}$.
Infinite springs with force constant $k$, $2k$, $4k$ and $8k$.... respectively are connected in series. The effective force constant of the spring will be
A system of two identical rods ($L-$ shaped) of mass $m$ and length $l$ are resting on a peg $P$ as shown in the figure. If the system is displaced in its plane by a small angle $\theta ,$ find the period of oscillations :
A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20\; m/s^2$ at a distance of $5\; m$ from the mean position. The time period of oscillation is
A weightless spring which has a force constant oscillates with frequency $n$ when a mass $m$ is suspended from it. The spring is cut into two equal halves and a mass $2m $ is suspended from it. The frequency of oscillation will now become