A particle of mass $200 \,gm$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N / m$. The time period of oscillations is .... $\sec$
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The potential energy of a simple harmonic oscillator of mass $2\, kg$ in its mean position is $5\, J.$ If its total energy is $9\,J$ and its amplitude is $0.01\, m,$ its time period would be
The displacement of a particle from its mean position (in metre) is given by $y = 0.2\sin (10\pi t + 1.5\pi )\cos (10\pi t + 1.5\pi )$. The motion of particle is
Two springs, of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$ If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes
The displacement time graph of a particle executing $S.H.M.$ is given in figure: (sketch is schematic and not to scale) Which of the following statements is are true for this motion?
$(A)$ The force is zero $t=\frac{3 T}{4}$
$(B)$ The acceleration is maximum at $t=T$
$(C)$ The speed is maximum at $t =\frac{ T }{4}$
$(D)$ The $P.E.$ is equal to $K.E.$ of the oscillation at $t=\frac{T}{2}$
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
A mass $m$ is attached to two springs of same force constant $K$, as shown in following four arrangements. If $T_1, T_2, T_3$ and $T_4$ respectively be the time periods of oscillation in the following arrangements, in which case time period is maximum?
A block of mass $2\,kg$ is attached with two identical springs of spring constant $20\,N / m$ each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $\frac{\pi}{\sqrt{x}}$ in SI unit. The value of $x$ is $..........$
A man is swinging on a swing made of $2$ ropes of equal length $L$ and in direction perpendicular to the plane of paper. The time period of the small oscillations about the mean position is
A body executes simple harmonic motion under the action of a force $F_1$ with a time period $(4/5)\, sec$. If the force is changed to $F_2$ it executes $SHM$ with time period $(3/5)\, sec$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body, its time period (in $seconds$ ) is