Correct Answer - Option 1 : v
max = Aω at mean position
CONCEPT:
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Simple harmonic motion occurs when the restoring force is directly proportional to the displacement from equilibrium.
F α -x
Where F = force and x = the displacement from equilibrium.
The equation of displacement in SHM is given by:
x = A sin(ωt + ϕ) .........(i)
where x is the distance from the mean position at any time t, A is amplitude, t is time, and ω is the angular frequency.
The equation of velocity in SHM is given by:
v = Aω cos(ωt + ϕ)
or \(v = ω √{A^2-x^2}\)
where v is the velocity at any time t or displacement x, A is amplitude, t is time, and ω is the angular frequency.
EXPLANATION:
The equation of velocity in SHM is given by:
\(v= ω \sqrt(A^2-x^2) \)
the max value of v in this equation can be obtained when x = 0
\(v= ω \sqrt(A^2-0^2) \)
vmax = Aω
And x = 0 means mean position or equilibrium position.
So at the mean position, the speed of a particle executing SHM is maximum and its value is Aω.
Hence the correct answer is option 4.
