The acceleration of a body executing simple harmonic motion leads the velocity by what phase?
A)"0 rad
B)"$\pi$/8 rad"
C)"$\pi$/4 rad"
D)"$\pi$/2 rad"
E)"$\pi$ rad"

Question

Quizplus · Accepted Answer

In simple harmonic motion, acceleration is given by the formula a=-ω^2x, where ω is the angular frequency and x is the displacement. Velocity, on the other hand, is given by the formula v=dx/dt. Taking the derivative of the displacement equation x=Acos(ωt+φ), where A is the amplitude and φ is the phase constant, we get v=-ωAsin(ωt+φ). By comparing the two equations, we can see that the velocity lags behind the acceleration by a phase angle of π/2 or 90 degrees. In radians, this is equal to ωt+φ=F1F1F1S1π/2=F1F1F1S1πF1F1F10/2 rad, which simplifies to F1F1F1S1πF1F1F10/2 rad. Therefore, the correct choice is D.

The Acceleration of a Body Executing Simple Harmonic Motion Leads π\piπ

The Acceleration of a Body Executing Simple Harmonic Motion Leads $\pi$