A simple harmonic oscillator has an amplitude a and time period $T$. The time required by it to travel from $x = a$ to $x = \frac{a }{2}$ is
  • A$T / 6$
  • B$T / 4$
  • C$T / 3$
  • D$T / 2$
AIPMT 1992, Medium
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
    The velocity-time diagram of a harmonic oscillator is shown in the adjoining figure. The frequency of oscillation is ..... $Hz$
    View Solution
  • 2
    If the period of oscillation of mass $m$ suspended from a spring is $2\, sec$, then the period of mass $4m$ will be  .... $\sec$
    View Solution
  • 3
    Time period of a particle executing $SHM$ is $8\, sec.$ At $t = 0$ it is at the mean position. The ratio of the distance covered by the particle in the $1^{st}$ second to the $2^{nd}$ second is :
    View Solution
  • 4
    A uniform thin ring of radius $R$ and mass $m$ suspended in a vertical plane from a point in its circumference. Its time period of oscillation is ........
    View Solution
  • 5
    A particle of mass $m$ undergoes oscillations about $x=0$ in a potential given by $V(x)-\frac{1}{2} k x^2-V_0 \cos \left(\frac{x}{a}\right)$, where $V_0, k, a$ are constants. If the amplitude of oscillation is much smaller than $a$, the time period is given by
    View Solution
  • 6
    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
  • 7
    A block of mass $m$ rests on a platform. The platform is given up and down $SHM$ with an amplitude $d$ . What can be the maximum frequency so that the block never leaves the platform
    View Solution
  • 8
    A body of mass $m $ is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass $m$ is slightly pulled down and released , it oscillates with a time period of $3\,s$ . When the mass $m$ is increased by $1\,kg$ , the time period of oscillations becomes $5\,s$ . The value of $m$ in $kg$ is
    View Solution
  • 9
    The time period of a particle executing $S.H.M.$ is $8 \,s$. At $t=0$ it is at the mean position. The ratio of distance covered by the particle in $1^{\text {st }}$ second to the $2^{\text {nd }}$ second is .............. $s$
    View Solution
  • 10
    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