For a particle executing $S.H.M.$ the displacement $x$ is given by $x = A\cos \omega t$. Identify the graph which represents the variation of potential energy $(P.E.)$ as a function of time $t$ and displacement $x$
  • A$I, III$
  • B$II, IV$
  • C$II, III$
  • D$I, IV$
IIT 2003, Medium
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 particle of mass $m$ is located in a one dimensional potential field where potential energy is given by : $V(x) = A(1 -cos\, px)$ ,

    where $A$ and $p$ are constant.

    The period of small oscillations of the particle is

    View Solution
  • 2
    The time period of a simple pendulum is $2\, sec$. If its length is increased $4$ times, then its period becomes  ..... $\sec$
    View Solution
  • 3
    The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T$.The period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury and $T_3$ when it is half filled with mercury. Which of the following is true
    View Solution
  • 4
    A simple pendulum has time period $T$. The bob is given negative charge and surface below it is given positive charge. The new time period will be
    View Solution
  • 5
    For a particle executing $S.H.M.,\, x =$ displacement from equilibrium position, $v =$ velocity at any instant and $a =$ acceleration at any instant, then
    View Solution
  • 6
    The phase of a particle executing simple harmonic motion is $\frac{\pi }{2}$ when it has
    View Solution
  • 7
    Length of a simple pendulum is $l$ and its maximum angular displacement is $\theta$, then its maximum $K.E.$ is
    View Solution
  • 8
    Values of the acceleration $A$ of a particle moving in simple harmonic motion as a function of its displacement $x$ are given in the table below. The period of the motion is

    $A (mm \,\,s^{-2}$)

     $16$

        $8$

    $0$

    $- 8$

    $- 16$

    $x\;(mm)$

    $- 4$

    $- 2$

    $0$

      $2$

       $4$

    View Solution
  • 9
    A particle in $SHM $ is described by the displacement equation $x(t) = A\cos (\omega t + \theta ).$ If the initial $(t = 0)$ position of the particle is $1 \,cm$ and its initial velocity is $\pi $cm/s, what is its amplitude? The angular frequency of the particle is $\pi {s^{ - 1}}$
    View Solution
  • 10
    What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of $10\,cm$ ($g = 9.8\, m/s^2$) ..... $m/s$
    View Solution