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Question:

If maximum speed of a particle in SHM is given by Vm. What is its average speed?

πVm2

2Vmπ

πVm4

Vm√2

Solution:

Let the SHM be represented as x = A sin(ωt + φ)
Thus the speed of a particle = dx/dt = |Aωcos(ωt + φ)| ⇒ Vm = Aω
The average speed of the particle = ∫₀^(2π/ω)|Aωcos(ωt + φ)| dt / (2π/ω) = 2Aω/π = 2Vm/π