The angular frequency of the damped oscillator is given by, $\omega  = \sqrt {\left( {\frac{k}{m} - \frac{{{r^2}}}{{4{m^2}}}} \right)} $ where $k$ is the spring constant, $m$ is the mass of the oscillator and $r$ is the damping constant. If the ratio $\frac{{{r^2}}}{{mk}}$ is $8\%$, the change in time period compared to the undamped oscillator is approximately as follows
  • Aincreases by $1\%$
  • Bincreases by $8\%$
  • Cdecreases by $1\%$ 
  • Ddecreases by $8\%$
JEE MAIN 2014, 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
    In forced oscillations, a particle oscillates simple harmonically with a frequency equal to
    View Solution
  • 2
    A body of mass $1\,kg$ is executing simple harmonic motion. Its displacement $y(cm)$ at $t$ seconds is given by $y = 6\sin (100t + \pi /4)$. Its maximum kinetic energy is ..... $J$
    View Solution
  • 3
    The displacement of a particle executing periodic motion is given by :
    $y = 4cos^2\,(t/2)sin\,(1000t)$
    This expression may be considered to be a result of superposition of
    View Solution
  • 4
    Which of the following is a necessary and sufficient condition for S.H.M.
    View Solution
  • 5
    The displacement y of a particle executing periodic motion is given by $y = 4{\cos ^2}(t/2)\sin (1000t)$. This expression may be considered to be a result of the superposition of ........... independent harmonic motions
    View Solution
  • 6
    Identify correct statement among the following
    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 point particle is acted upon by a restoring force $-k x^{3}$. The time-period of oscillation is $T$, when the amplitude is $A$. The time-period for an amplitude $2 A$ will be
    View Solution
  • 9
    Astone is swinging in a horizontal circle $0.8\, m$ in diameter at $30 \,rev / min.$ Adistant horizontal light beam causes a shadow of the stone to be formed on a nearly vertical wall. The amplitude and period of the simple harmonic motion for the shadow of the stone are
    View Solution
  • 10
    In an experiment to determine the period of a simple pendulum of length $1\, m$, it is attached to different spherical bobs of radii $r_1$ and $r_2$ . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be $5\times10^{-4}\, s$, the difference in radii, $\left| {{r_1} - {r_2}} \right|$ is best given by .... $cm$
    View Solution