A $0.10\, kg$ block oscillates back and forth along a horizontal surface. Its displacement from the origin is given by: $x = (10\,cm)\cos [(10\,rad/s)\,t + \pi /2\,rad]$. What is the maximum acceleration experienced by the block
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A flat horizontal board moves up and down in $SHM$ of amplitude $\alpha$. Then the shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board 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 $10\,cm$ ($g = 9.8\, m/s^2$) ..... $m/s$
Two identical balls A and B each of mass 0.1 kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radius 0.06 m. Each spring has a natural length of 0.06$\pi$ m and force constant 0.1N/m. Initially both the balls are displaced by an angle $\theta = \pi /6$ radian with respect to the diameter $PQ$ of the circle and released from rest. The frequency of oscillation of the ball B is
The maximum potential energy of a block executing simple harmonic motion is $25\,J$. A is amplitude of oscillation. At $A / 2$, the kinetic energy of the block is $...............$
A simple harmonic motion is represented by $y\, = 5\,(\sin \,3\pi t\, + \,\sqrt 3 \,\cos \,3\pi t)\,cm$ The amplitude and time period of the motion are
$Assertion :$ In $SHM$, acceleration is always directed towards the mean position.
$Reason :$ In $SHM$, the body has to stop momentary at the extreme position and move back to mean position.