What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless ?
Advanced
Download our app for free and get startedPlay store
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}_{\mathrm{eq}}}}$

$\mathrm{F}_{\mathrm{net}}=-(4 \mathrm{k})(4 \mathrm{x})=-16 \mathrm{kx}$

$\Rightarrow \mathrm{k}_{\mathrm{eq}}=16 \mathrm{K}$

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
    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
  • 2
    If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is:
    View Solution
  • 3
    The displacement of a particle executing $S.H.M.$ is given by $x=0.01 \sin 100 \pi(t+0.05)$. The time period is ........ $s$
    View Solution
  • 4
    Time period of a simple pendulum is $T$. The time taken to complete $5 / 8$ oscillations starting from mean position is $\frac{\alpha}{\beta} T$. The value of $\alpha$ is ..... .
    View Solution
  • 5
    A particle executes simple harmonic motion. Its amplitude is $8 \,cm$ and time period is $6 \,s$. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ............. $s$
    View Solution
  • 6
    A spring is stretched by $5 \,\mathrm{~cm}$ by a force $10 \,\mathrm{~N}$. The time period of the oscillations when a mass of $2 \,\mathrm{~kg}$ is suspended by it is :(in $s$)
    View Solution
  • 7
    A pendulum with time period of $1\, s$ is losing energy due to damping. At certain time its energy is $45\, J$. If after  completing $15\,oscillations$ , its energy has become $15\, J$, its damping constant (in $s^{-1}$ ) is
    View Solution
  • 8
    A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is $\frac{2 \mathrm{~A}}{3}$. The new amplitude of motion is $\frac{\mathrm{nA}}{3}$. The value of $\mathrm{n}$ is____.
    View Solution
  • 9
    A particle executing $S.H.M.$ of amplitude 4 cm and $T = 4 \,sec.$ The time taken by it to move from positive extreme position to half the amplitude is ..... $\sec$
    View Solution
  • 10
    A body oscillates with $S.H.M.$ according to the equation $x=(5.0 \,m ) \cos \left[\left(2 \pi \,rad s ^{-1}\right) t+\pi / 4\right]$ At $t=1.5 \,s$, its acceleration is ....... $m / s ^2$
    View Solution