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
JEE MAIN 2014, Medium
Download our app for free and get startedPlay store
The change in time period compared to the undamped oscillator increases by $1\%$
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 displacement of a particle along the $x-$ axis is given by $x=asin^2$$\omega t$ . The motion of the particle corresponds to 
    View Solution
  • 2
    A particle of mass $200 \,gm$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N / m$. The time period of oscillations is .... $\sec$
    View Solution
  • 3
    A particle of mass $m$ is attached to three identical springs $A, B$ and $C$ each of force constant $ k$ a shown in figure. If the particle of mass $m$ is pushed slightly against the spring $A$ and released then the time period of oscillations is
    View Solution
  • 4
    A particle executing simple harmonic motion has an amplitude of $6\, cm$. Its acceleration at a distance of $2 \,cm$ from the mean position is $8\,cm/{s^2}$. The maximum speed of the particle is ... $ cm/s$
    View Solution
  • 5
    A mass $0.9\,kg$, attached to a horizontal spring, executes $SHM$ with an amplitude $A _{1}$. When this mass passes through its mean position, then a smaller mass of $124\,g$ is placed over it and both masses move together with amplitude $A _{2}$. If the ratio $\frac{ A _{1}}{ A _{2}}$ is $\frac{\alpha}{\alpha-1}$, then the value of $\alpha$ will be$......$
    View Solution
  • 6
    The length of a spring is $l$ and its force constant is $k$. When a weight $W$ is suspended from it, its length increases by $x$. If the spring is cut into two equal parts and put in parallel and the same weight $W$ is suspended from them, then the extension will be
    View Solution
  • 7
    A $3\ kg$ sphere dropped through air has a terminal speed of $25\ m/s$. (Assume that the drag force is $-bv$.) Now suppose the sphere is attached to a spring of force constant $k = 300\ N/m$, and that it oscillates with an initial amplitude of $20\ cm$. What is the angular frequencu of its damped $SHM$? ..... $rad/s$
    View Solution
  • 8
    The length of simple pendulum is increased by $44\%$. The percentage increase in its time period will be ..... $\%$
    View Solution
  • 9
    A body executes simple harmonic motion. The potential energy $(P.E.)$, the kinetic energy $(K.E.)$ and total energy $(T.E.)$ are measured as a function of displacement $x$. Which of the following statements is true
    View Solution
  • 10
    A simple harmonic motion having an amplitude $A$ and time period $T$ is represented by the equation : $y = 5 \sin \pi (t + 4) m$

    Then the values of $A$ (in $m$) and $T$ (in $sec$) are :

    View Solution