Question

A damped harmonic oscillator loses 8 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency f₀ = (1/2?)?k/m?

Answer 1

For damped harmonic motion A= Ao e st Here r= 6/2m wiek z I wo 11- 11 J m After one period energy decreases to 8%. E = 0.92Eo 4 KA² = 0.9 (1KA) IK (Aperty2 = 0.98 ( 2 KA0² one-280 = 0.92 -28T = ln (0.92 w a re = -I in 60.92) = 0.04169-(1) w-wo Wo di 19.) - W Wo Wo - wo هلیا

in cq. o becomes wl-wo a 1 1 - 1 1 1 I 1-187 12 - : wo wo w'-wo, a 2.205x10-5 % difference (wh- wo ) lov = (2-205x105 100 of difference = 0.0022%) I wo

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