A particle of mass $10\, gm$ is describing $S.H.M.$ along a straight line with period of $2\, sec$ and amplitude of $10, cm$. Its kinetic energy when it is at $5 \,cm$ from its equilibrium position is
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When a mass $m$ is hung from the lower end of a spring of neglibgible mass, an extension $x$ is produced in the spring. The time period of oscillation is
This is the position time graph of a mass on spring. What can you say about the velocity and force at the instant indicated by dashed line ? (positive direction is to the right)
A particle executes simple harmonic motion with an amplitude of $4 \mathrm{~cm}$. At the mean position, velocity of the particle is $10 \mathrm{~cm} / \mathrm{s}$. The distance of the particle from the mean position when its speed becomes $5 \mathrm{~cm} / \mathrm{s}$ is $\sqrt{\alpha} \mathrm{cm}$, where $\alpha=$____________.
A particle executes $SHM$ on a straight line path. The amplitude of oscillation is $2\, cm.$ When the displacement of the particle from the mean position is $1\, cm,$ the numerical value of magnitude of acceleration is equal to the numerical value of magnitude of velocity. The frequency of $SHM$ (in $second^{-1}$) is :
Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated in the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ is
A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K _1$ and $K _2$. For the frictionless surface, the time period of oscillation of mass $m$ is
A body of mass $m $ is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass $m$ is slightly pulled down and released , it oscillates with a time period of $3\,s$ . When the mass $m$ is increased by $1\,kg$ , the time period of oscillations becomes $5\,s$ . The value of $m$ in $kg$ is
A simple pendulum oscillates freely between points $A$ and $B$. We now put a peg (nail) at the point $C$ as shown in above figure. As the pendulum moves from $A$ to the right, the string will bend at $C$ and the pendulum will go to its extreme point $D$. Ignoring friction, the point $D$
A particle moves in the $x-y$ plane according to equation $\overrightarrow r = (\widehat i + 2\widehat j)\, A \, \cos \omega t$. The motion of the particle is