The amplitude of an oscillating simple pendulum is $10\,cm$ and its period is $4\, sec$. Its speed after $1\, sec$ after it passes its equilibrium position, is ... $m/s$
Easy
Download our app for free and get startedPlay store
(a) At the time $t = \frac{T}{4} = \frac{4}{4} = 1\sec $ after passing from mean position, the body reaches at it's extreme position. At extreme, position velocity of body becomes zero.
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 free to move along the $x-$axis has potential energy given by $U(x) = k[1 - \exp {( - x)^2}]$ for $ - \infty \le x \le + \infty $, where k is a positive constant of appropriate dimensions. Then
    View Solution
  • 2
    A man weighing $60\  kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\  m$ and frequency $\frac{2}{\pi } Hz$. Which of the following staements is correct
    View Solution
  • 3
    A mass of $5\, {kg}$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4\, {m}$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed? (In ${m} / {s}^{2}$)
    View Solution
  • 4
    An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and the cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_ 0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
    View Solution
  • 5
    Out of the following functions representing motion of a particle which represents $SHM$ 

    $(A)\;y= sin\omega t-cos\omega t$

    $(B)\;y=sin^3\omega t$

    $(C)\;y=5cos\left( {\frac{{3\pi }}{4} - 3\omega t} \right)$

    $(D)\;y=1+\omega t+{\omega ^2}{t^2}$

    View Solution
  • 6
    A simple pendulum oscillates in air with time period $T$ and amplitude $A$. As the time passes
    View Solution
  • 7
    The phase difference between two $SHM\,\,$  ${y_1}\, = \,10\,\sin \,\left( {10\pi t\, + \,\frac{\pi }{3}} \right)$ and ${y_2}\, = \,12\,\sin \,\left( {8\pi t\, + \,\frac{\pi }{4}} \right)$  at $t = 0.5\,s$ it
    View Solution
  • 8
    The general displacement of a simple harmonic oscillator is $x = A \sin \omega t$. Let $T$ be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when $t=\frac{T}{\beta}$. The value of $\beta$ is $.........$
    View Solution
  • 9
    A particle of unit mass is moving along the $x$-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column $I$ (a and $U _0$ are constants). Match the potential energies in column $I$ to the corresponding statement$(s)$ in column $II.$

    column $I$ column $II$
    $(A)$ $U _1( x )=\frac{ U _0}{2}\left[1-\left(\frac{ x }{ a }\right)^2\right]^2$ $(P)$ The force acting on the particle is zero at $x = a$.
    $(B)$ $U _2( x )=\frac{ U _0}{2}\left(\frac{ x }{ a }\right)^2$ $(Q)$ The force acting on the particle is zero at $x=0$.
    $(C)$ $U _3( x )=\frac{ U _0}{2}\left(\frac{ x }{ a }\right)^2 \exp \left[-\left(\frac{ x }{ a }\right)^2\right]$ $(R)$ The force acting on the particle is zero at $x =- a$.
    $(D)$ $U _4( x )=\frac{ U _0}{2}\left[\frac{ x }{ a }-\frac{1}{3}\left(\frac{ x }{ a }\right)^3\right]$ $(S)$ The particle experiences an attractive force towards $x =0$ in the region $| x |< a$.
      $(T)$ The particle with total energy $\frac{ U _0}{4}$ can oscillate about the point $x=-a$.

     

    View Solution
  • 10
    A particle of mass $m$ is attached to one end of a mass-less spring of force constant $k$, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t=0$ with an initial velocity $u_0$. When the speed of the particle is $0.5 u_0$, it collies elastically with a rigid wall. After this collision :

    $(A)$ the speed of the particle when it returns to its equilibrium position is $u_0$.

    $(B)$ the time at which the particle passes through the equilibrium position for the first time is $t=\pi \sqrt{\frac{ m }{ k }}$.

    $(C)$ the time at which the maximum compression of the spring occurs is $t =\frac{4 \pi}{3} \sqrt{\frac{ m }{ k }}$.

    $(D)$ the time at which the particle passes througout the equilibrium position for the second time is $t=\frac{5 \pi}{3} \sqrt{\frac{ m }{ k }}$.

    View Solution