A mass $m$ is suspended by means of two coiled spring which have the same length in unstretched condition as in figure. Their force constant are $k_1$ and $k_2$ respectively. When set into vertical vibrations, the period will be
  • A$2\pi \sqrt {\left( {\frac{m}{{{k_1}{k_2}}}} \right)} $
  • B$2\pi \sqrt {m\left( {\frac{{{k_1}}}{{{k_2}}}} \right)} $
  • C$2\pi \sqrt {\left( {\frac{m}{{{k_1} - {k_2}}}} \right)} $
  • D$2\pi \sqrt {\left( {\frac{m}{{{k_1} + {k_2}}}} \right)} $
Easy
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
    You are holding a shallow circular container of radius $R$, filled with water to a height $h ( h < < R )$. When yon walk with speed $v$, it is seen that water starts spilling over. This happens due to the resonance of the periodic impulse given to the container (due to walking) with the oscillation of the water in the container. If the time period of water oscillating in the container is inversely proportional to $\sqrt{ h }$, then $v$ is proportional to
    View Solution
  • 2
    A mass $m$ attached to a spring oscillates every $2\, sec$. If the mass is increased by $2 \,kg$, then time-period increases by $1\, sec$. The initial mass is ..... $kg$
    View Solution
  • 3
    If $x, v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T$, then, which of the following does not change with time?
    View Solution
  • 4
    A horizontal platform with an object placed on it is executing $S.H.M$. in the vertical direction. The amplitude of oscillation is $3.92 \times {10^{ - 3}}m$. What must be the least period of these oscillations, so that the object is not detached from the platform
    View Solution
  • 5
    The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is
    View Solution
  • 6
    Two simple harmonic motion, are represented by the equations ${y}_{1}=10 \sin \left(3 \pi {t}+\frac{\pi}{3}\right)$

    $y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)$

    Ratio of amplitude of ${y}_{1}$ to ${y}_{2}={x}: 1$. The value of ${x}$ is ...... .

    View Solution
  • 7
    A particle performs $SHM$ on $x-$ axis with time period of $0.5\,sec,$ such that it's velocity is zero at $x = -3\,cm$ and at $x = 9\,cm$. It was located at $x = 0$ and moving in negative $'x'$ at $t = 0$. The equation of $SHM$ of the particle is
    View Solution
  • 8
    What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless ?
    View Solution
  • 9
    A body of mass $5\; kg$ hangs from a spring and oscillates with a time period of $2\pi $ seconds. If the ball is removed, the length of the spring will decrease by
    View Solution
  • 10
    Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ is
    View Solution