Displacement-time equation of a particle executing $SHM$ is $x\, = \,A\,\sin \,\left( {\omega t\, + \,\frac{\pi }{6}} \right)$ Time taken by the particle to go directly from $x\, = \, - \frac{A}{2}$ to $x\, = \, + \frac{A}{2}$ is
Advanced
Download our app for free and get started
displacement, $X=A \sin \left(\omega t+\frac{\pi}{6}\right)$
At $X=-\frac{A}{2}$
$-\frac{A}{2}=A \sin \left(\omega t_{1}+\frac{\pi}{6}\right)$
$\omega t_{1}+\frac{\pi}{6}=\sin ^{-1}(-0.5)$
$\omega t_{1}+\frac{\pi}{6}=-\frac{\pi}{6}$
$t_{1}=-\frac{\pi}{3 \omega} \ldots .(1)$
At $X=+\frac{A}{2}$
$\frac{A}{2}=A \sin \left(\omega t_{2}+\frac{\pi}{6}\right)$
$\omega t_{2}+\frac{\pi}{6}=\sin ^{-1}(0.5)$
$\omega t_{2}+\frac{\pi}{6}=\frac{\pi}{6}$
$\omega t_{2}=0$
$t_{2}=0 \ldots \ldots .(2)$
The time taken by the particle,
$T=t_{2}-t_{1}$
$T=0-\left(-\frac{\pi}{3 \omega}\right)$
$T=\frac{\pi}{3 \omega}$
The correct option is $A.$
Download our appand get started for free
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.*
Similar Questions
- 1A pendulum with time period of $1\, s$ is losing energy due to damping. At certain time its energy is $45\, J$. If after completing $15\,oscillations$ , its energy has become $15\, J$, its damping constant (in $s^{-1}$ ) isView Solution
- 2The potential energy of a particle executing S.H.M. is $ 2.5\, J$, when its displacement is half of amplitude. The total energy of the particle be .... $J$View Solution
- 3The maximum velocity of a simple harmonic motion represented by $y = 3\sin \,\left( {100\,t + \frac{\pi }{6}} \right)$is given byView Solution
- 4A block of mass $m$ is at rest on an another block of same mass as shown in figure. Lower block is attached to the spring, then the maximum amplitude of motion so that both the block will remain in contact isView Solution
- 5A 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 $s$)View Solution
- 6Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass $=500\, g$, Decay constant $=20 \,g / s$ then ...... $s$ time is required for the amplitude of the system to drop to half of its initial value ? $(\ln 2=0.693)$View Solution
- 7A small body of mass $0.10\, kg$ is executing $S.H.M.$ of amplitude $1.0 \,m$ and period $0.20\, sec$. The maximum force acting on it is.... $N$View Solution
- 8View SolutionFor the system given below, find the angular frequency of oscillation ?
- 9The instantaneous displacement of a simple pendulum oscillator is given by $x = A\cos \left( {\omega t + \frac{\pi }{4}} \right)$. Its speed will be maximum at timeView Solution
- 10A particle free to move along the $x-$axis has potential energy given by $U(x) = k[1 - \exp {( - x)^2}]$ for $ - \infty \le x \le + \infty $, where k is a positive constant of appropriate dimensions. ThenView Solution