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Differential equations assignment T6

  1. Dec 4, 2013 #1
    Hi!

    I would like to ask anyone with some spare time to check my assignment questions. Last time I was asked to post one task at a time so I will.
    Thank you in advance for your time.

    Task 6:

    In a galvanometer the deflection θ satisfies the diffrential equation:

    d2θ/dt2+2(dθ/dt)+θ=4

    Solve the equation for θ given that when t=0, θ=0 and dθ/dt=0


    Solution:

    d2θ/dt2+2(dθ/dt)+θ=4

    m2+2m+1=0

    m=-1

    CF:
    ∴u=(At+B)e-t

    PI:
    v=k
    v'=0
    v''=0

    k+2(0)+0=4
    k=4
    ∴v=4

    GS:
    θ=(At+B)e-t+4

    0=(A(0)+B)e0+4
    0=B+4
    B=-4

    dθ/dt=(At-4)(-e-t)+Ae-t
    0=(A(0)-4)(-e0)+Ae0
    0=4+A
    A=-4

    PS:
    θ=(-4t-4)e-t+4
     
  2. jcsd
  3. Dec 4, 2013 #2

    jedishrfu

    Staff: Mentor

    Why don't you check them yourself and show what you did?
     
  4. Dec 4, 2013 #3
    I'm not sure if it's right but that's how I checked it:

    θ=(At+B)e-t+4
    dθ/dt=(At+B)(-e-t)+Ae-t
    d2θ/dt2=(At+B)(e-t)+A(-e-t)-Ae-t

    t=0
    θ=0
    dθ/dt=0
    A=-4
    B=-4

    [d2θ/dt2=(At+B)(e-t)+A(-e-t)-Ae-t]+2[0]+[(At+B)e-t+4]=4

    -4+4+4-4+4=4
     
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