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Two small bodies of mass of $2\, kg$ each attached to each other using a thread of length $10\, cm$, hang on a spring whose force constant is $200\, N/m$, as shown in the figure. We burn the thread. What is the distance between the two bodies when the top body first arrives at its highest position .... $cm$ ? (Take $\pi^2 = 10$)
A man weighing $60\, kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\, m$ and frequency $\frac{2}{\pi }Hz$. Which of the following statement is correct
The instantaneous displacement of a simple pendulum oscillator is given by $x = A\cos \left( {\omega t + \frac{\pi }{4}} \right)$. Its speed will be maximum at time
A particle of mass $m$ in a unidirectional potential field have potential energy $U(x)=\alpha+2 \beta x^2$, where $\alpha$ and $\beta$ are positive constants. Find its time period of oscillation.
The amplitude and the time period in a $S.H.M.$ is $0.5 \,cm$ and $0.4 \,sec$ respectively. If the initial phase is $\pi /2$ radian, then the equation of $S.H.M.$ will be
The scale of a spring balance reading from $0$ to $10 \,kg$ is $0.25\, m$ long. A body suspended from the balance oscillates vertically with a period of $\pi /10$ second. The mass suspended is ..... $kg$ (neglect the mass of the spring)