Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i...

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Transcript of Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i...

Page 1: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse

Waves  Revision  

Page 2: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 3: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 4: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 5: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 6: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 7: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 8: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 9: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 10: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 11: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 12: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 13: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 14: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse

Sep  2012,  Q3  

And  remember  v=ω/k  

Page 15: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 16: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 17: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 18: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 19: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 20: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 21: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 22: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 23: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse

y(x,t) = (Acoskx+Bsinkx)(Ccoskct + Dsinkct)

Or  e.g.  d’Alambert      y(x,t)  =  Asin(kx  -­‐  ω  t)  +  Bsin(kx  +  ωt)    

Page 24: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse
Page 25: Waves&Revision& - University of Oxford · A' T (kl —k2) —im02 A T (kl + k2) + iú)2m 2klT + + i 02m 3. Consider a taut string of mass per unit length PI which carries transverse

Numerical Methods for Partial D-MATH Differential ... · mufinal = RadTEvl(u0,mesh,Tfinal,m) that carries out m uniform timesteps of the L-stable SDIRK-2 implicit 2-stage Runge-Kutta

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