Differential equation

  • Thread starter dan5
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  • #1
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Homework Statement



y'' + 24y' +432y = cos (wt)

yp(x) = R(h) cos (ht - ∅(h))

find R(h)
and hbar = value for h which R(h) is max.
and ∅(hbar)

Homework Equations



double angle formula for cos
cos (a-b) = cos a cos b + sin a sin b

The Attempt at a Solution



solving the equation as a quadratic in coefficients on sin and cos, hbar = 12

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
HallsofIvy
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Frankly, I can't figure out what your question is. What is yp? Is it supposed to be a particular solution? If so, you will need to find yp' and yp'' and put them into the equation. What do you get when you do that?
 
  • #3
9
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yes yp is the particular solution.

Well i thought of using a trial particular solution of

yp= A sin (Ht) + B cos (Ht)

which leaves me with

-AH2-24BH+432A = 0 for coefficients of sin(Ht)

and

-BH2+24AH+432B = 1 for coefficients of cos(Ht)
 

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