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In college physics, the phase of velocity vibration of spring oscillator lags behind the acceleration. Why is this sentence right?
x=A*cos (ωt+φ)

v = dx/dt =-aω* sin(ωt+φ)= aω* cos(ωt+φ+π/2)

a=dv/dt=-aω^2*sin(ωt+φ+π/2)=-aω^2*cos(ωt+φ+π)

Therefore, the phase of velocity lags behind the phase of acceleration π/2.