Lecture 8 Notes

8 case 2 0 f0 0 x cos0 t m xp t ta cos0

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Unformatted text preview: cos(ω0 t) + C2 sin(ω0 t) • Case 1: ω ￿= ω0 xp (t) = A cos(ω t) + B sin(ω t) ￿￿ 2 2 xp (t) = −ω A cos(ω t) − ω B sin(ω t) 2 ￿￿ mxp + kxp = (k − ω m)A cos(ω t) + ω0 = ￿ k m natural frequency (k − ω m)B sin(ω t) F0 = F0 cos(ω t) ⇒ A = 2 − ω2 ) , B = 0 m(ω0 2 Forced vibrations (3.8) • Case 2: ω = ω0 Forced vibrations (3.8) • Case 2: ω = ω0 mx + kx = F0 cos(ω0 t) ￿￿ ω0 = ￿ k m Forced vibrations (3.8) • Case 2: x+ ￿￿ ω = ω0 2 ω0 x F0 = cos(ω0 t) m ω0 = ￿ k m Forced vibrations (3.8) • Case 2: ω = ω0 F0 ω0 = x+ = cos(ω0 t) m xp (t) = t(A cos(ω0 t) + B sin(ω0 t)) ￿￿ 2 ω0 x ￿ k m Forced vibrations (3.8) • Case 2: ω = ω0 F0 ω0 = x+ = cos(ω0 t) m xp (t) = t(A cos(ω0 t) + B sin(ω0 t)) ￿￿ ￿ xp (t) 2 ω0 x = A cos(ω0 t) + B sin(ω0 t) ￿ k m Forced vibrations (3.8) • Case 2: ω = ω0 F0 ω0 = x+ = cos(ω0 t) m xp (t) = t(A cos(ω0 t) + B sin(ω0 t)) ￿￿ ￿ xp (t) 2 ω0 x ￿ k m = A cos(ω0 t) + B sin(ω0 t) +t(−ω0 A sin(ω0 t) + ω0 B cos(ω0 t)) Forced vibrations (3.8) • Case 2: ω = ω0 F0 ω0 = x+ = cos(ω0 t) m xp (t) = t(A cos(ω0 t) + B sin(ω0 t)) ￿￿ ￿ xp (t) 2 ω0 x ￿ k m = A cos(ω0 t) + B sin(ω0 t) +t(−ω0 A sin(ω0 t) + ω0 B cos(ω0 t)) x￿￿ (t) = −ω0 A sin(ω0 t) + ω0 B cos(ω0 t) p Forced vibrations (3.8) • Case 2: ω = ω0 F0 ω0 = x+ = cos(ω0 t) m xp (t) = t(A cos(ω0 t) + B sin(ω0 t)) ￿￿ ￿ xp (t) 2 ω0 x ￿ k m = A cos(ω0 t) + B sin(ω0 t) +t(−ω0 A sin(ω0 t) + ω0 B cos(ω0 t)) x￿￿ (t) = −ω0 A sin(ω0 t) + ω0 B cos(ω0 t) p +(−ω0 A sin(ω0 t) + ω0 B cos(ω0 t)) Forced vibrations (3.8) • Case 2: ω = ω0 F0 ω0 = x+ = cos(ω0 t) m xp (t) = t(A cos(ω0 t) + B sin(ω0 t)) ￿￿ ￿ xp (t) 2 ω0 x ￿ k m = A cos(ω0 t) + B sin(ω0 t) +t(−ω0 A sin(ω0...
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