A $LCR$ circuit behaves like a damped harmonic oscillator. Comparing it with a physical springmass damped oscillator having damping constant $\mathrm{b}$, the correct equivalence would be:
JEE MAIN 2020, Diffcult
Download our app for free and get startedPlay store
By $kVL$

$-\mathrm{L} \frac{\mathrm{di}}{\mathrm{dt}}-\frac{\mathrm{q}}{\mathrm{C}}-\mathrm{iR}=0$

$\mathrm{L} \frac{\mathrm{d}^{2} \mathrm{q}}{\mathrm{dt}^{2}}+\frac{1}{\mathrm{C}} \mathrm{q}+\mathrm{R} \frac{\mathrm{dq}}{\mathrm{dt}}=0$

for damped oscillator

net force $=-\mathrm{kx}-\mathrm{bv}=\mathrm{ma}$

$\frac{m d^{2} x}{d t^{2}}+k x+\frac{b d x}{d t}=0$

by comparing : Equivalence is

$\mathrm{L} \rightarrow \mathrm{m}: \mathrm{C} \rightarrow \frac{1}{\mathrm{K}} ; \mathrm{R} \rightarrow \mathrm{b}$

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 phase (at a time $t$) of a particle in simple harmonic motion tells
    View Solution
  • 2
    Two springs of force constants $K$ and $2K$ are connected to a mass as shown below. The frequency of oscillation of the mass is
    View Solution
  • 3
    The angular amplitude of a simple pendulum is $\theta_0$. The maximum tension in its string will be
    View Solution
  • 4
    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
  • 5
    Which one of the following statements is true for the speed $v$ and the acceleration $a$ of a particle executing simple harmonic motion
    View Solution
  • 6
    A particle executing $SHM$ of amplitude $4\,cm$ and $T = 4s.$ The time taken by it to move from $+2\,cm$ to $+2\sqrt 3\,cm$ is
    View Solution
  • 7
    A mass $m$ attached to a spring oscillates with a period of $3\,s$. If the mass is increased by $1\,kg$ the period increases by $1\,s$. The initial mass $m$ is
    View Solution
  • 8
    A simple pendulum consisting of a ball of mass $m$ tied to a thread of length $l$ is made to swing on a circular arc of angle $\theta $ in a vertical plane. At the end of this arc, another ball of mass $m$ is placed at rest. The momentum transferred to this ball at rest by the swinging ball is
    View Solution
  • 9
    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
  • 10
    Two simple pendulum whose lengths are $1\,m$ and $121\, cm$ are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum will the two be in phase again
    View Solution