A particle of mass m executes simple harmonic motion with amplitude a and frequency . The average kinetic energy during its motion from the position o - Physics MCQ AIEEE 2007 2026 | ExamTest.live

mediumMCQAIEEE 20072026Physics

1 attempts0% success rate1 mark

A particle of mass m executes simple harmonic motion with amplitude a and frequency ν . The average kinetic energy during its motion from the position of equilibrium to the end (one-quarter cycle) is:

Solution & Step-by-step Explanation

Velocity in SHM is v = aω cos ω t .Kinetic Energy K E = \frac{1}{2} m v^{2} = \frac{1}{2} m (aω)^{2} cos^{2} ω t .Average value of cos^{2} θ over a quarter cycle [0, π /2] is \frac{1}{2} .Average K E = \frac{1}{2} m a^{2} ω^{2} \times \frac{1}{2} = \frac{1}{4} m a^{2} ω^{2} .Given ω = 2 π ν :Average K E = \frac{1}{4} m a^{2} (2 π ν)^{2} = \frac{1}{4} m a^{2} (4 π^{2} ν^{2}) Average K E = π^{2} m a^{2} ν^{2}

Try it yourself before checking the explanation above.

A particle of mass m executes simple harmonic motion with amplitude a and frequency ν . The average kinetic energy during its motion from the position of equilibrium to the end (one-quarter cycle) is:

π^{2} m a^{2} ν^{2}

\frac{1}{4} π^{2} m a^{2} ν^{2}

4 π^{2} m a^{2} ν^{2}

2 π^{2} m a^{2} ν^{2}

Practice with timed mock tests and track your performance across Physics.