Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to $A$ and $T,$  respectively. At time $t=0$ one particle has displacement $A$ while the other one has displacement $\frac {-A}{2}$ and they are moving towards each other. If they cross each other at time $t,$ then $t$ is
  • A$\frac{{5T}}{6}$
  • B$\frac{{T}}{3}$
  • C$\frac{{T}}{4}$
  • D$\frac{{T}}{6}$
JEE MAIN 2016, Diffcult
art

Download our app
and 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

  • 1
    A circular disc of mass $10 \;kg$ is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be $1.5 \;s$. The radius of the disc is $15\; cm .$ Determine the torsional spring constant of the wire in $N\;m\;rad^{-1}$. (Torsional spring constant $\alpha$ is defined by the relation $J=-\alpha \theta,$ where $J$ is the restoring couple and $\theta$ the angle of twist).
    View Solution
  • 2
    Two particles oscillating in $SHM$ along two very close parallel path such that they have same mean position. The equation of $SHM$ of two particles are $x_1 = A\, sin\,\omega t$ and $x_2 = A\,sin(\omega t + \phi )$ respectively. If maximum distance between them is $\frac{6A}{5}$ then $\phi $ equal to ..... $^o$
    View Solution
  • 3
    One-forth length of a spring of force constant $K$ is cut away. The force constant of the remaining spring will be
    View Solution
  • 4
    Two simple harmonic motion, are represented by the equations ${y}_{1}=10 \sin \left(3 \pi {t}+\frac{\pi}{3}\right)$

    $y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)$

    Ratio of amplitude of ${y}_{1}$ to ${y}_{2}={x}: 1$. The value of ${x}$ is ...... .

    View Solution
  • 5
    A simple harmonic wave having an amplitude a and time period $T$ is represented by the equation $y = 5\sin \pi (t + 4)m.$ Then the value of amplitude $(a)$ in $(m)$ and time period $(T) $ in second are
    View Solution
  • 6
    The $S.H.M.$ of a particle is given by the equations $=2 \sin \omega t+4 \cos \omega t$. Its amplitude of oscillation is ........ units
    View Solution
  • 7
    A particle is executing simple harmonic motion with a time period $T.$ At time $t = 0$, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like
    View Solution
  • 8
    A simple harmonic motion is represented by $F(t) = 10\sin \,(20\,t + 0.5)$. The amplitude of the $S.H.M.$ is  $a$ $=$ .... 
    View Solution
  • 9
    There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum is
    View Solution
  • 10
    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
    View Solution