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What is the time period of kinetic energy of a particle in SHM,if the time period of SHM is 4s?
  • a)
    2s
  • b)
    1s
  • c)
    4s
  • d)
    0s
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
What is the time period of kinetic energy of a particle in SHM,if the ...
The kinetic energy of a particle in SHM is given by:
0.5mA2w2cos2(wt + a), where a is the phase constant.
cos2(wt + a) = (1 + cos2(wt+a))/2.
Therefore the time period of oscillation of kinetic energy is 4/2 = 2s.
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Community Answer
What is the time period of kinetic energy of a particle in SHM,if the ...
The time period of simple harmonic motion (SHM) is the time taken for one complete cycle of the motion. In the case of a particle in SHM, the time period is given as 4 seconds.

To find the time period of the kinetic energy of the particle, we need to understand the relationship between the position and kinetic energy of the particle in SHM.

In SHM, the particle oscillates back and forth about a mean position, and its position can be described by a sine or cosine function. The kinetic energy of the particle is given by the equation:

KE = (1/2)mv^2

where KE is the kinetic energy, m is the mass of the particle, and v is the velocity of the particle.

Since the velocity of the particle is greatest when it passes through the mean position and zero when it reaches the extreme positions, the kinetic energy is also maximum at the mean position and zero at the extreme positions.

Based on this understanding, we can conclude that the time period of the kinetic energy of the particle in SHM is equal to the time period of the motion itself.

Therefore, if the time period of the SHM is 4 seconds, the time period of the kinetic energy of the particle will also be 4 seconds.

Hence, the correct answer is option 'A' - 2s.
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