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Math Help - (Laplace)Need explainations

  1. #1
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    (Laplace)Need explainations

    hey guys need some explanation on these: the red arrows indicates the part where i do not understand how the eqn derive to the other eqn. (see picture 3)

    And maybe if you can also explain the "pattern" of the t>1, 1<t<2, 2<t<4 ...you know what i mean,if the question changes. i am having a problem looking at the "switch" function.
    Q1





    Q2


    Q3
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  2. #2
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    Quote Originally Posted by mathsnerd View Post
    hey guys need some explanation on these: the red arrows indicates the part where i do not understand how the eqn derive to the other eqn. (see picture 3)

    And maybe if you can also explain the "pattern" of the t>1, 1<t<2, 2<t<4 ...you know what i mean,if the question changes. i am having a problem looking at the "switch" function.
    Q1

    The first of these involves regrouping the terms so:

    <br />
(e^{-10t}-e^{-20t})-2(e^{-10(t-2)}-e^{-20(t-2)})=e^{-10t}-2e^{-10(t-2)}-e^{-20t}+2e^{-20(t-2)}<br />

    ........ <br />
= (e^{-10t}-2e^{-10(t-2)})-(e^{-20t}-2e^{-20(t-2)})=e^{-10t}(1-2e^{20})-e^{-20t}[1-2e^{-40})<br />

    The second requires that you distribute the derivative over the difference in the
    square barckets, then differentiate the exponential terms dependent on t.

    RonL
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  3. #3
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    Quote Originally Posted by mathsnerd View Post

    Q2
    for 1<t<2,\ u(t)=1, and u(t-2)=0

    (look up the definition of Heaviside's or the unit step function u(t) if need be).


    for t>2,\ u(t)=1, and u(t-2)=1.

    RonL
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  4. #4
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    Quote Originally Posted by mathsnerd View Post

    Q3
    Use: 30 = \frac{1200}{40} then rearrange

    RonL
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  5. #5
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    Thanks Ron. That was a fast reply.
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