Time period of a simple pendulum is $T$. The angular displacement for amplitude is $\beta$. How much time the bob of pendulum will take to move from equilibrium position $O$ to $A$, making an angle $\alpha$ at the support
  • A$T\,{\sin ^{ - 1}}\left( {\frac{\alpha }{\beta }} \right)$
  • B$T\,{\sin ^{ - 1}}\left( {\frac{\beta }{\alpha }} \right)$
  • C$\frac{T}{2\pi }\,{\sin ^{ - 1}}\left( {\frac{\alpha }{\beta }} \right)$
  • D$\frac{T}{\pi }\,{\sin ^{ - 1}}\left( {\frac{\alpha }{\beta }} \right)$
Diffcult
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 mass $m$ is attached to two springs of same force constant $K$, as shown in following four arrangements. If $T_1, T_2, T_3$ and $T_4$ respectively be the time periods of oscillation in the following arrangements, in which case time period is maximum?
    View Solution
  • 2
    Two parallel discs are connected by a rigid rod of length $L=0.5 \,m$ centrally. Each disc has a slit oppositely placed as shown in the figure. A beam of neutral atoms are incident on one of the discs axially at different velocities $v$, while the system is rotated at angular speed of $600 \,rev / second$, so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds (in metre/second) of the atoms that will emerge at the other end.
    View Solution
  • 3
    Two simple pendulums of length $1\, m$ and $4\, m$ respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed number of oscillations equal to
    View Solution
  • 4
    In the arrangement, spring constant $k$ has value $2\,N\,m^{-1}$ , mass $M = 3\,kg$ and mass $m = 1\,kg$ . Mass $M$ is in contact with a smooth surface. The coefficient of friction between two blocks is $0.1$ . The time period of $SHM$ executed by the system is
    View Solution
  • 5
    A second's pendulum is placed in a space laboratory orbiting around the earth at a height $3R$, where $R$ is the radius of the earth. The time period of the pendulum is
    View Solution
  • 6
    For a particle executing $S.H.M.,\, x =$ displacement from equilibrium position, $v =$ velocity at any instant and $a =$ acceleration at any instant, then
    View Solution
  • 7
    The total energy of a particle, executing simple harmonic motion is
    View Solution
  • 8
    The angular frequency of the damped oscillator is given by, $\omega  = \sqrt {\left( {\frac{k}{m} - \frac{{{r^2}}}{{4{m^2}}}} \right)} $ where $k$ is the spring constant, $m$ is the mass of the oscillator and $r$ is the damping constant. If the ratio $\frac{{{r^2}}}{{mk}}$ is $8\%$, the change in time period compared to the undamped oscillator is approximately as follows
    View Solution
  • 9
    The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement (amplitude = $a$) is
    View Solution
  • 10
    A simple pendulum of length $l$ and mass $m$ of the bob is suspended in a car that is travelling with a constant speed $v$ around a circular path of radius $R$. If the pendulum undergoes oscillations with small amplitude about its equilibrium position, the frequency of its oscillations will be
    View Solution