The angular velocity and the amplitude of a simple pendulum is $\omega $ and $a$ respectively. At a displacement $X$ from the mean position if its kinetic energy is $T$ and potential energy is $V$, then the ratio of $T$ to $V$ is
  • A${X^2}{\omega ^2}/({a^2} - {X^2}{\omega ^2})$
  • B${X^2}/({a^2} - {X^2})$
  • C$({a^2} - {X^2}{\omega ^2})/{X^2}{\omega ^2}$
  • D$({a^2} - {X^2})/{X^2}$
AIPMT 1991, 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
    The amplitude of a wave represented by displacement equation

    $y = \frac{1}{{\sqrt a }}\,\sin \,\omega t \pm \frac{1}{{\sqrt b }}\,\cos \,\omega t$ will be

    View Solution
  • 2
    For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $1\,kg$, the angular frequency is $\omega_1$. When the mass block is $2\,kg$ the angular frequency is $\omega_2$. The ratio $\omega_2 / \omega_1$ is
    View Solution
  • 3
    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
    View Solution
  • 4
    A particle performs $SHM$ about $x = 0$ such that at $t = 0$ it is at $x = 0$ and moving towards positive extreme. The time taken by it to go from $x = 0$ to $x = \frac{A}{2}$ is ..... times the time taken to go from $x = \frac{A}{2}$ to $A$. The most suitable option for the blank space is
    View Solution
  • 5
    A uniform rod of length $2.0 \,m$ is suspended through an end and is set into oscillation with small amplitude under gravity. The time period of oscillation is approximately .... $\sec$
    View Solution
  • 6
    Time period of a particle executing $SHM$ is $8\, sec.$ At $t = 0$ it is at the mean position. The ratio of the distance covered by the particle in the $1^{st}$ second to the $2^{nd}$ second is :
    View Solution
  • 7
    Three simple harmonic motions of equal amplitudes $A$ and equal time periods in the same direction combine. The phase of the second motion is $60^o$ ahead of the first and the phase of the third motion is $60^o$ ahead of the second. Find the amplitude of the resultant motion
    View Solution
  • 8
    The acceleration of a particle performing S.H.M. is at a distance of $3\; cm$ from the mean position is $ 12\,cm/sec^2 $. Its time period is ..... $\sec$
    View Solution
  • 9
    The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is
    View Solution
  • 10
    Which of the following expressions corresponds to simple harmonic motion along a straight line, where $x$ is the displacement and $a, b, c$ are positive constants?
    View Solution