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Math Help - Derivation and Integration Numerical

  1. #1
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    Derivation and Integration Numerical

    Consider a signal function of time in the form:
    t=0:0.005:10
    y=(2sin(2 \pi t)exp(-0.1t)+0.2cos(20 \pi t)) / (4-0.1t+0.2sin(10 \pi t))

    How to derive two times the signal y?
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  2. #2
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    If your code is MATLAB source, Please type:

    >> syms t
    >> y=(2*sin(2*pi*t)*exp(-0.1*t)+0.2*cos(20 *pi* t)) / (4-0.1*t+0.2*sin(10 *pi *t))
    >> diff(y, 2)
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  3. #3
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    Quote Originally Posted by math2009 View Post
    If your code is MATLAB source, Please type:

    >> syms t
    >> y=(2*sin(2*pi*t)*exp(-0.1*t)+0.2*cos(20 *pi* t)) / (4-0.1*t+0.2*sin(10 *pi *t))
    >> diff(y, 2)
    I need to know how to calculate by hand
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  4. #4
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    I guess I have to get a polynomial interpolation and derive this polynomial.
    How can I get the polynomial interpolation of this function?
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  5. #5
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    I found the 1st derivative:

    y | 0 | 0.005 | 10
    f(t) | 0.05 | 0.0503 | 0.2271

    Newton interpolation:

    F[x_0 , x_1] = \frac{f(x_1)-f(x_0)}{x_1 - x_0} = 0.06

    F[x_0,x_1,x_2] = -4.231x10^{-3}

    p(x) = f(x_0)+(x-x_0)F[x_0,x_1]+(x-x_0)(x-x_1)F[x_0,x_1,x_2]
    p(x) = -4.231x10^{-3}x^2 + 0.06021x + 0.05

    f'(t) = p'(x)
    f'(t) = 8.462x10^{-3}x + 0.06021

    Is correct ?
    For the second derivative I need to interpolate again?
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  6. #6
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    I have an observation in this exercise that I did not understand.
    OBS: Use 0.005s step to derive
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