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The piston in the cylinder head of locomotive has a stroke of $6\,m$ (which is twice the amplitude). If the piston executing simple harmonic motion with an angular frequency of $200\, rad\, min^{-1}$, its maximum speed is .... $ms^{-1}$
A load of mass $m$ falls from a height $h$ on to the scale pan hung from the spring as shown in the figure. If the spring constant is $k$ and mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is
A particle moves in the $x-y$ plane according to equation $\overrightarrow r = (\widehat i + 2\widehat j)\, A \, \cos \omega t$. The motion of the particle is
A damped harmonic oscillator has a frequency of $5$ oscillations per second. The amplitude drops to half its value for every $10$ oscillations. The time it will take to drop to $\frac{1}{1000}$ of the original amplitude is close to .... $s$
Two simple harmonic motions are represented by equations ${y_1} = 4\,\sin \,\left( {10t + \phi } \right)$ and ${y_2} = 5\,\cos \,10\,t$ What is the phase difference between their velocities?
The period of a simple pendulum measured inside a stationary lift is found to be $T$. If the lift starts accelerating upwards with acceleration of $g/3,$ then the time period of the pendulum is
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 angular frequency of a spring block system is $\omega _0.$ This system is suspended from the ceiling of an elevator moving downwards with a constant speed $v_0.$ The block is at rest relative to the elevator. Lift is suddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement :