A horizontal platform with an object placed on it is executing $S.H.M$. in the vertical direction. The amplitude of oscillation is $3.92 \times {10^{ - 3}}m$. What must be the least period of these oscillations, so that the object is not detached from the platform
A$0.1256\, sec$
B$0.1356\, sec$
C$0.1456\, sec$
D$0.1556\, sec$
AIIMS 1999, Diffcult
Download our app for free and get started
A$0.1256\, sec$
a (a) By drawing free body diagram of object during the downward motion at extreme position, for equilibrium of mass
$mg - R = mA$ ($A = $ Acceleration)
For critical condition $R = 0$
so $mg = mA$
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
A particle is executing $S.H.M.$ with time period $T^{\prime}$. If time period of its total mechanical energy is $T$ then $\frac{T^{\prime}}{T}$ is ........
Two light identical springs of spring constant $k$ are attached horizontally at the two ends of a uniform horizontal rod $AB$ of length $l$ and mass $m$. the rod is pivoted at its centre $‘O’$ and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is
A particle is oscillating according to the equation $X = 7\cos 0.5\pi t$, where $t$ is in second. The point moves from the position of equilibrium to maximum displacement in time ..... $\sec$
Two damped spring-mass oscillating systems have identical spring constants and decay times. However, system $A's$ mass $m_A$ is twice system $B's$ mass $m_B$ . How do their damping constants, $b$ , compare ?
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
For a particle executing $S.H.M.$ the displacement $x$ is given by $x = A\cos \omega t$. Identify the graph which represents the variation of potential energy $(P.E.)$ as a function of time $t$ and displacement $x$
A point mass oscillates along the x-axis according to the law $x=x_0cos$$\left( {\omega t - \frac{\pi }{4}} \right)$ If the acceleration of the particle is written as $a=Acos$$\left( {\omega t + \delta } \right)$ then