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A particle executes simple harmonic oscillation with an amplitude $a.$ The period of oscillation is $T.$ The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
Two particles are executing $SHM$ of the same amplitude $A$ and frequency $\omega $ along the $x-$ axis. Their mean position is separated by $X_0$ (where $X_0 > A$ ). If maximum separation between them is $X_0 + 2A$ , then the phase difference between their motion is
Two particles execute $SHM$ of same amplitude of $20\, cm$ with same period along the same line about the same equilibrium position. The maximum distance between the two is $20\, cm.$ Their phase difference in radians is
A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is $\frac{2 \mathrm{~A}}{3}$. The new amplitude of motion is $\frac{\mathrm{nA}}{3}$. The value of $\mathrm{n}$ is____.
An object of mass $0.5\, {kg}$ is executing simple harmonic motion. Its amplitude is $5\, {cm}$ and time period (T) is $0.2\, {s} .$ What will be the potential energy of the object at an instant $t=\frac{T}{4}$ s starting from mean position. Assume that the initial phase of the oscillation is zero. (In ${J}$)
A mass m performs oscillations of period $T$ when hanged by spring of force constant $K$. If spring is cut in two parts and arranged in parallel and same mass is oscillated by them, then the new time period will be
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 $t=\frac{T}{2}$
In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_{1}$ of the force, while the energy is maximum for a frequency $\omega_{2}$ of the force, then
The scale of a spring balance reading from $0$ to $10 \,kg$ is $0.25\, m$ long. A body suspended from the balance oscillates vertically with a period of $\pi /10$ second. The mass suspended is ..... $kg$ (neglect the mass of the spring)