In the given figure, a body of mass $M$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k,$ the frequency of oscillation of given body is :
JEE MAIN 2021, Diffcult
Download our app for free and get startedPlay store
$K _{ eq }= K _{1}+ K _{2}= K + K =2 K$

$T =2 \pi \sqrt{\frac{ m }{ K _{ eq }}}=2 \pi \sqrt{\frac{ m }{2 K }}$

$f =\frac{1}{ T }=\frac{1}{2 \pi} \sqrt{\frac{2 K }{ m }}$

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 $K.E.$ and $P.E.$ of a particle executing $SHM$ with amplitude $A$ will be equal when its displacement is
    View Solution
  • 2
    A body oscillates with a simple harmonic motion having amplitude $0.05\, m .$ At a certain instant, its displacement is $0.01\, m$ and acceleration is $1.0 \,m / s ^{2} .$ The period of oscillation is
    View Solution
  • 3
    For a body executing $S.H.M. :$

    $(a)$ Potential energy is always equal to its $K.E.$

    $(b)$ Average potential and kinetic energy over any given time interval are always equal.

    $(c)$ Sum of the kinetic and potential energy at any point of time is constant.

    $(d)$ Average $K.E.$ in one time period is equal to average potential energy in one time period.

    Choose the most appropriate option from the options given below:

    View Solution
  • 4
    An object of mass $0.2\  kg$ executes simple harmonic along $X-$ axis with frequency of $\frac{{25}}{\pi } Hz$ . At the position $x$ =  $0.04\ m$ , the object has kinetic energy of $0.5\  J$ and potential energy of $0.4\  J$ amplitude of oscillation in meter is equal to
    View Solution
  • 5
    In arrangement given in figure, if the block of mass m is displaced, the frequency is given by
    View Solution
  • 6
    A pendulum clock that keeps correct time on the earth is taken to the moon it will run (it is given that $g_{Moon} = g_{Earth}/6$ )
    View Solution
  • 7
    The angular frequency of a spring block system is $\omega _0.$ This system is suspended from the ceiling of an elevator moving downwards with a constant speed $v_0.$ The block is at rest relative to the elevator. Lift is suddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement :
    View Solution
  • 8
    A spring of force constant $k$ is cut into lengths of ratio $1:2:3$ . They are connected in series and the new force constant is $k'$ . Then they are connected in parallel and force constant is $k''$ . Then $k':k''$ is
    View Solution
  • 9
    A particle executes $S.H.M.$ and its position varies with time as $x=A$ sin $\omega t$. Its average speed during its motion from mean position to mid-point of mean and extreme position is
    View Solution
  • 10
    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 $10cm$  ......... $m/s$ (Take $g = 9.8\,m/{s^2})$
    View Solution