If the period of oscillation of mass $m$ suspended from a spring is $2\, sec$, then the period of mass $4m$ will be  .... $\sec$
AIIMS 1998, Medium
Download our app for free and get startedPlay store
(d) $T = 2\pi \sqrt {\frac{m}{k}} $

==>$\frac{{{T_2}}}{{{T_1}}} = \sqrt {\frac{{{m_2}}}{{{m_1}}}} = \sqrt {\frac{{4m}}{m}} = 2$

$ \Rightarrow {T_2} = 2 \times 2 = 4\;s$

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
    A particle performs $SHM$ about $x = 0$ such that at $t = 0$ it is at $x = 0$ and moving towards positive extreme. The time taken by it to go from $x = 0$ to $x = \frac{A}{2}$ is ..... times the time taken to go from $x = \frac{A}{2}$ to $A$. The most suitable option for the blank space is
    View Solution
  • 2
    The force-deformation equation for a nonlinear spring fixed at one end is $F =4x^{1/ 2}$  , where $F$ is the force (expressed in newtons) applied at the other end and $x$ is the deformation expressed in meters
    View Solution
  • 3
    The displacement $x$ (in metres) of a particle performing simple harmonic motion is related to time $t$ (in seconds) as $x = 0.05\cos \left( {4\,\pi \,t + \frac{\pi }{4}} \right)$. The frequency of the motion will be ..... $Hz$
    View Solution
  • 4
    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
  • 5
    Consider the following statements. The total energy of a particle executing simple harmonic motion depends on its

    $(1)$ Amplitude      $(2) $ Period         $(3)$ Displacement

    Of these statements

    View Solution
  • 6
    A block is resting on a piston which executes simple harmonic motion with a period $2.0 \,s$. The maximum velocity of the piston, at an amplitude just sufficient for the block to separate from the piston is .......... $ms ^{-1}$
    View Solution
  • 7
    Which of the following expressions corresponds to simple harmonic motion along a straight line, where $x$ is the displacement and $a, b, c$ are positive constants?
    View Solution
  • 8
    The drawing shows a top view of a frictionless horizontal surface, where there are two indentical springs with particles of mass $m_1$ and $m_2$ attached to them. Each spring has a spring constant of $1200\  N/m.$ The particles are pulled to the right and then released from the  positions shown in the drawing. How much time passes before the particles are again side by side for the first time if $m_1 = 3.0\  kg$ and $m_2 = 27 \,kg \,?$
    View Solution
  • 9
    An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross$-$section, $A$. Young modulus of the material of the wire is $Y$. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is
    View Solution
  • 10
    The $ P.E.$ of a particle executing $SHM$ at a distance $x$ from its equilibrium position is
    View Solution