The total mechanical energy of a particle in $SHM$ is
  • A
    Always constant
  • B
    Depend on time
  • C$\frac{1}{2}\,K{A^2}\,{\cos ^2}\,(\omega t\, + \,\phi )$
  • D$\frac{1}{2}\,m{A^2}\,{\cos ^2}\,(\omega t\, + \,\phi )$
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
    Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies $\omega_1$ and $\omega_2$ and have total energies $E_1$ and $E_2$, respectively. The variations of their momenta $p$ with positions $x$ are shown in the figures. If $\frac{a}{b}= n ^2$ and $\frac{ a }{ R }= n$, then the correct equation$(s)$ is(are) $Image$

    $(A)$ $E_1 \omega_1=E_2 \omega_2$ $(B)$ $\frac{\omega_2}{\omega_1}=n^2$ $(C)$ $\omega_1 \omega_2= n ^2$ $(D)$ $\frac{E_1}{\omega_1}=\frac{E_2}{\omega_2}$

    View Solution
  • 2
    A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is $\frac{2}{{\sqrt 5 }}$. After how many collisions the amplitude of vibration will become less than $60°$
    View Solution
  • 3
    When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\frac{x}{8}$, where $x=$_____________.
    View Solution
  • 4
    A particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the  position of the particle as a function of time $?$
    View Solution
  • 5
    The angular velocity and the amplitude of a simple pendulum is $'\omega '$ and $'A'$ respectively. At a displacement $x$ from the mean position its kinetic energy is $'T'$ and potnetial energy is $'V'$. Then the ratio $\frac{V}{T}$ is
    View Solution
  • 6
    A particle executes linear simple harmonic motion with an amplitude of $2\, cm$. When the particle is at $1\, cm$ from the mean position the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is
    View Solution
  • 7
    A particle is executing simple harmonic motion with an amplitude of $0.02$ metre and frequency $50\, Hz$. The maximum acceleration of the particle is
    View Solution
  • 8
    If the time period of a two meter long simple pendulum is $2\, s$, the acceleration due to gravity at the place where pendulum is executing $S.H.M.$ is
    View Solution
  • 9
    A plank with a small block on top of it is under going vertical $SHM.$ Its period is $2\, sec.$ The minimum amplitude at which the block will separate from plank is :
    View Solution
  • 10
    The total energy of particle performing $S.H.M.$ depend on
    View Solution