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Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass $=500\, g$, Decay constant $=20 \,g / s$ then ...... $s$ time is required for the amplitude of the system to drop to half of its initial value ? $(\ln 2=0.693)$
A simple pendulum with a metallic bob has a time period $T$. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is $1 / 4$ that of metal, the time period of the same pendulum will be ...........
Two particles execute $SHM$ of same amplitude of $20\, cm$ with same period along the same line about the same equilibrium position. The maximum distance between the two is $20\, cm.$ Their phase difference in radians is
What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of $10cm$ ......... $m/s$ (Take $g = 9.8\,m/{s^2})$
A mass $m$ is attached to two springs of same force constant $K$, as shown in following four arrangements. If $T_1, T_2, T_3$ and $T_4$ respectively be the time periods of oscillation in the following arrangements, in which case time period is maximum?
A particle executing simple harmonic motion has an amplitude of $6\, cm$. Its acceleration at a distance of $2 \,cm$ from the mean position is $8\,cm/{s^2}$. The maximum speed of the particle is ... $ cm/s$
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is $10\,s^{-1}$. At, $t = 0$ the displacement is $5\, m$. What is the maximum acceleration ? The initial phase is $\frac{\pi }{4}$
A particle of mass $m$ oscillates with simple harmonic motion between points ${x_1}$ and ${x_2}$, the equilibrium position being $O$. Its potential energy is plotted. It will be as given below in the graph