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    Hi, I have been asked this question...

    A dynamical system is modelled by the equation

    \ddot{x}(t) + 3\dot{x}(t) + 2x(t) = f(t)

    where f(t) is an impulse of strength 3 units applied at t=4 and is subject to the initial conditions

    x(0) = 2 and \dot{x}(0) = -4

    Find an expression for x in terms of t

    I am little confused as to how I would start. I know i need to write it f(t) as the dirac delta function, but I don't know how to do this. I can do the rest of the calculations.
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    (Original post by PerigeeApogee)
    Have you studied Laplace Transforms?

    If so, that would, without doubt, be the easiest way to approach the problem. If not, let me know.
    yeah thats what I'm going to use to solve this. But in lectures, we have always written f(t) in the form of the dirac delta function. I know how to solve it but I just need to change f(t) to dirac delta.
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    Well, \delta(t) is an impulse of strength 1 unit applied when t = 0...
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    oh i see.
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    (Original post by PerigeeApogee)
    Or, as Franklin says....  f(t) = 4 \delta (t+4)
    At least a couple of errors there, but note also that I wanted the OP to find the expression for herself.
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    (Original post by DFranklin)
    At least a couple of errors there, but note also that I wanted the OP to find the expression for herself.
    would it not be,

    f(t) = 3 \delta (t-4)
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    Yes, exactly.
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    (Original post by DFranklin)
    Yes, exactly.
    Thanks very much. I can do the rest of the calculations from ghere xxx
 
 
 
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