Energy Decay For Undamped harmonic oscillator: E=-mi2+=kx2=-ka2og(constant) For Underdamped oscillator Cma(t)=amaz(O)e-Sun Thus, we expect E(t)=E(Oe-2sant valid for lightly damped systems This can be used to estimate s if Energy (decay) can be measuredEnergy Decay For Undamped harmonic oscillator: E = 1 2 mx˙ 2 + 1 2 kx2 = 1 2 kx2 max (constant) For Underdamped oscillator xmax(t) = xmax(0)e −ζωnt Thus, we expect E(t) = E(0)e −2ζωnt . . . valid for lightly damped systems This can be used to estimate ζ if Energy (decay) can be measured. 6