A mass on a vertical spring begins its motion at rest at $y = 0\ cm$. It reaches a maximum height of $y = 10\ cm$. The two forces acting on the mass are gravity and the spring force. The graph of its kinetic energy ($KE$) versus position is given below. Net force on the mass varies with $y$ as
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The displacement of a body executing $SHM$ is given by $x = A \sin (2\pi t + \pi /3).$ The first time from $t = 0$ when the velocity is maximum is .... $\sec$
A mass $m = 1.0\,kg$ is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is $500\,N/m.$ What is the amplitude $A$ of the motion, so that the mass $m$ tends to get detached from the pan ? (Take $g = 10\,m/s^2$ ). The spring is stiff enough so that it does not get distorted during the motion.
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 $10\,cm$ ($g = 9.8\, m/s^2$) ..... $m/s$
A particle executing $S.H.M.$ of amplitude 4 cm and $T = 4 \,sec.$ The time taken by it to move from positive extreme position to half the amplitude is ..... $\sec$
Consider a one-dimensional potential $V(x)$ as shown in the figure below. A classical particle of mass $m$ moves under its influence and has total energy $E$ as shown below. The motion is
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