Question

The solution to the initial value problem below takes on different forms for different ranges of the parameter ζ, which is called the dimensionless damping coefficient. In each case, write the solution in the suggested form. u'' + 6 ζ u' +9u = 0 u(0) = 0 u'(0) = 1 If ζ > 1 , uζ(t) = e( Incorrect: Your answer is incorrect. ) sinh( Incorrect: Your answer is incorrect. ) Incorrect: Your answer is incorrect. Compute the limit as ζ→ 1+ : lim ζ→1+ uζ= Incorrect: Your answer is incorrect. If ζ < 1 , uζ(t) = e( ) sin( ) Compute the limit as ζ→ 1− : lim ζ→1− uζ= Find the general solution to the differential equation in the case ζ = 1 , u1(t) = Now find the solution to the initial value problem when ζ = 1 . u1(t) =

The solution to the initial value problem below takes on different forms for different ranges of the parameter , which is called the dimensionless damping coefficient. In each case, write the solution in the suggested forn u(o) 0 >1, u'(0)= 1 If ur(t) = e compute the limit as 7→ 1+· lim uoo sin u(t)e Compute the limit as : lim up -1 Find the general solution to the differential equation in the case Now find the solution to the initial value problem when 〈 1. u1(t) =

Answer 1

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