Download App
$m x^{2}-b x+k=0$

Find time after which to the energy will become half of initial maximum value in damped force oscillation.

  • A$t=\frac{m}{b}+\frac{1}{2} \ln 2$
  • B$t=\frac{m}{b} \times \frac{2}{3} \ln 2$
  • C$t=\frac{m}{b}-\frac{1}{2} \ln 2$
  • D$t=\frac{m}{b} \times \frac{1}{2} \ln 2$
AIIMS 2019, 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.*
Download App

Similar Questions

  • 1
    The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended, the period of oscillation will now be
    View Solution
  • 2
    The height of liquid column in a $U$ tube is $0.3$ meter. If the liquid in one of the limbs is depressed and then released, then the time period of liquid column will be $.......\,sec$ 
    View Solution
  • 3
    A particle of mass $10 \,g$ is undergoing $S.H.M.$ of amplitude $10 \,cm$ and period $0.1 \,s$. The maximum value of force on particle is about ............ $N$
    View Solution
  • 4
    $Assertion :$ Resonance is a special case of forced vibration in which the natural frequency of vibration of the body is the same as the impressed frequency of external periodic force and the amplitude of forced vibration is maximum.
    $Reason :$ The amplitude of forced vibrations of a body increases with an increase in the frequency of the externally impressed periodic force.
    View Solution
  • 5
    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
  • 6
    A block of mass $m$ is attached to two springs of spring constants $k_1$ and $k_2$ as shown in figure. The block is displaced by $x$ towards right and released. The velocity of the block when it is at $x/2$ will be
    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 graph shows the variation of displacement of a particle executing S.H.M. with time. We infer from this graph that
    View Solution
  • 9
    The amplitude of vibration of a particle is given by ${a_m} = ({a_0})/(a{\omega ^2} - b\omega + c);$ where ${a_0},a,b$ and $c$ are positive. The condition for a single resonant frequency is
    View Solution
  • 10
    The time period of a particle executing $S.H.M.$ is $8 \,s$. At $t=0$ it is at the mean position. The ratio of distance covered by the particle in $1^{\text {st }}$ second to the $2^{\text {nd }}$ second is .............. $s$
    View Solution