Lecture 8 Notes

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online