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A body is executing simple harmonic motion with an angular frequency $2\,rad/s$. The velocity of the body at $20\, mm$ displacement, when the amplitude of motion is $60\, mm$, is ...... $mm/s$
A particle in $S.H.M.$ is described by the displacement function $x(t) = a\cos (\omega t + \theta )$. If the initial $(t = 0)$ position of the particle is $1\, cm $ and its initial velocity is $\pi \,cm/s$. The angular frequency of the particle is $\pi \,rad/s$, then it’s amplitude is
An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is $15\, cm/sec$ and the period is $628$ milli-seconds. The amplitude of the motion in centimeters is
On a planet a freely falling body takes $2 \,sec$ when it is dropped from a height of $8 \,m$, the time period of simple pendulum of length $1\, m$ on that planet is ..... $\sec$
Three masses $700g, 500g$ and $400g$ are suspended at the end of a spring a shown and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a period of $3\,seconds$, when the $500g$ mass is also removed, it will oscillate with a period of .... $s$