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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 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
Two, spring $P$ and $Q$ of force constants $k_p$ and ${k_Q}\left( {{k_Q} = \frac{{{k_p}}}{2}} \right)$ are stretched by applying forces of equal magnitude. If the energy stored in $Q$ is $E$, then the energy stored in $P$ is
A block of mass $200\, g$ executing $SHM$ under the influence of a spring of spring constant $K=90\, N\,m^{-1}$ and a damping constant $b=40\, g\,s^{-1}$. The time elapsed for its amplitude to drop to half of its initial value is ...... $s$ (Given $ln\,\frac{1}{2} = -0.693$)
The displacement of a particle moving in $S.H.M.$ at any instant is given by $y = a\sin \omega t$. The acceleration after time $t = \frac{T}{4}$ is (where $T$ is the time period)
The time period of a mass suspended from a spring is $T$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be
A clock $S$ is based on oscillations of a spring and a clock $P$ is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having same density as earth but twice the radius then
A $1 \,kg$ block attached to a spring vibrates with a frequency of $1\, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8\, kg$ block placed on the same table. So, the frequency of vibration of the $8\, kg$ block is ..... $Hz$