A damped harmonic oscillator of mass m it released at time t=0 and displaced by a distance xo. Show motion is described by the following second order differential equation mẍ + λẋ + m(ω_0^2)x=0; with ω_0^2=k/m For a lightly damped (λ<< ω_0) oscillator the quality factor (Q value), is defined as Q = (Energy (E) stored in the simple harmonic system)/(energy lost(E_lost) per radian of oscillation) Show that Q = ω_0/2λ Hint: Ue the trial solution x(t) =A exp(-λt)cos(ωt-δ)
A damped harmonic oscillator of mass m it released at time t=0 and displaced by a distance xo. Show motion is described by the following second order differential equation mẍ + λẋ + m(ω_0^2)x=0; with ω_0^2=k/m For a lightly damped (λ<< ω_0) oscillator the quality factor (Q value), is defined as Q = (Energy (E) stored in the simple harmonic system)/(energy lost(E_lost) per radian of oscillation) Show that Q = ω_0/2λ Hint: Ue the trial solution x(t) =A exp(-λt)cos(ωt-δ)
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A damped harmonic oscillator of mass m it released at time t=0 and displaced by a distance xo. Show motion is described by the following second order differential equation
mẍ + λẋ + m(ω_0^2)x=0; with ω_0^2=k/m
For a lightly damped (λ<< ω_0) oscillator the quality factor (Q value), is defined as
Q = (Energy (E) stored in the simple harmonic system)/(energy lost(E_lost) per radian of oscillation)
Show that Q = ω_0/2λ
Hint: Ue the trial solution x(t) =A exp(-λt)cos(ωt-δ)
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