At which point (place) does a particle executing $SHM$ have maximum kinetic energy and maximum potential energy?

  • A
    Maximum kinetic energy at mean position,maximum potential energy at extreme position.
  • B
    Maximum kinetic energy at extreme position,maximum potential energy at mean position.
  • C
    Maximum kinetic energy and potential energy both at mean position.
  • D
    Maximum kinetic energy and potential energy both at extreme position.

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$A$ particle starts oscillating simple harmonically from its equilibrium position with time period $T$. At time $t = \frac{T}{12}$,the ratio of its kinetic energy to potential energy is $\left[\sin \frac{\pi}{3} = \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}, \sin \frac{\pi}{6} = \cos \frac{\pi}{3} = \frac{1}{2}\right]$.

The displacements of two particles of same mass executing $SHM$ are represented by the equations $x_1=4 \sin \left(10 t+\frac{\pi}{6}\right)$ and $x_2=5 \cos (\omega t)$. The value of $\omega$ for which the energies of both the particles remain same is (in $\text{ unit}$)

$A$ linear harmonic oscillator of force constant $2 \times 10^6\, N/m$ and amplitude $0.01\, m$ has a total mechanical energy of $160\, J$. Which of the following statements is correct?

$A$ particle executes $SHM$ of amplitude $A$. The distance from the mean position when its kinetic energy becomes equal to its potential energy is:

The total energy of a particle,executing simple harmonic motion is

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