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Problem with an Undamped Forced Motion

  1. Oct 25, 2011 #1
    My professor assigned us a problem where
    m=16 lb
    k=10 lb/ft
    a=2
    t(0)=1 ft
    t'(0)=0 ft/sec

    Through this I determined the DE
    x''(t)+4x'(t)+20x(t)=e-t
    with initial conditions mentioned above.

    Using the method of m2+4m+20=0
    I got roots of -2±4i
    Therefore, my yc=e-2t[c1sin(4t)+c2cos(4t)]

    Next I attempted to solve further the problem, but I did not understand what to do as the examples I could find throughout the internet and my textbook all are regarding F(t)=cos(t) or similar.

    Any help or guidance would be appreciated. Unfortunately the problem is due tomorrow morning so any quick help is more preferred ;)

    Thanks :smile:,
    Matt!
     
  2. jcsd
  3. Oct 25, 2011 #2
    I managed to find
    c1=1/2
    c2=1

    So
    yc=e-2t((1/2)sin4t+cos4t)

    Now what to do :confused:
     
  4. Oct 25, 2011 #3
    I did some more work, can someone verify that this is correct please? :)

    21mg29f.jpg

    Thanks.
     
  5. Oct 25, 2011 #4
    Also, the graph I got from my general solution is provided by this link: "[URL [Broken]
     
    Last edited by a moderator: May 5, 2017
  6. Oct 26, 2011 #5
    I actually ended up getting y=(e^(-2x))((8/17)sin(4x)+(16/17)cos(4x))+(1/17)e^(-x)
    I hope this is right :).
     
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