An object moves in simple harmonic motion with amplitude 11m and period 4 minutes. At time t = 0 minutes, its displacement d from rest is - 11m, and initially, it moves in a positive direction. Give the equation modeling the displacement d as a function of time t. d = ?

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Conductor

Physics

3 March, 01:29

An object moves in simple harmonic motion with amplitude 11m and period 4 minutes. At time t = 0 minutes, its displacement d from rest is - 11m, and initially, it moves in a positive direction. Give the equation modeling the displacement d as a function of time t. d = ?

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Eden Bender · Answer 1

Angular velocity ω = 2π / T = 2 x 3. 14 / (4 x 60) =.026 rad / s.

d = D Sin (ωt + θ) where D = amplitude = 11 m θ = initial phase.

-11 = 11 sin (0 + θ) = sin θ = - 1, θ = - π / 2

So, d = D Sin (ωt - θ)

d = 11 Sin (.026 t - π / 2) is the required equation.