A spring is stretched by $5 \,\mathrm{~cm}$ by a force $10 \,\mathrm{~N}$. The time period of the oscillations when a mass of $2 \,\mathrm{~kg}$ is suspended by it is :(in $s$)
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A particle is performing simple harmonic motion along $x$ -axis with amplitude $4\, cm$ and time period $1.2\, sec$. The minimum time taken by the particle to move from $x = 2\, cm$ to $x =+ 4 \,cm$ and back again is given by .... $s$
The amplitude of a damped oscillator becomes one third in $2\, sec$. If its amplitude after $6\, sec$ is $1/n$ times the original amplitude then the value of $n$ is
The kinetic energy of a particle executing $S.H.M.$ is $16\, J$ when it is in its mean position. If the amplitude of oscillations is $25\, cm$ and the mass of the particle is $5.12\, kg$, the time period of its oscillation is
A particle is executing $SHM$ with amplitude $A,$ time period $T,$ maximum acceleration $a_o$ and maximum velocity $v_0.$ Its starts from mean position at $t=0$ and at time $t,$ it has the displacement $A/2,$ acceleration $a$ and velocity $v$ then
A particle performs simple harmonic motion with amplitude $A$. Its speed is trebled at the instant that it is at a distance $\frac{{2A}}{3}$ from equilibrium position. The new amplitude of the motion 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)
The periodic time of a body executing simple harmonic motion is $3\, sec$. After how much interval from time $t = 0$, its displacement will be half of its amplitude ..... $\sec$
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.
A uniform rod of length $2.0 \,m$ is suspended through an end and is set into oscillation with small amplitude under gravity. The time period of oscillation is approximately .... $\sec$