Question

1. Find the Laplace Transformation of the following function. First express the function in terms of $u_c(t)$. Then use #12 from the Laplace table. Do not use computer. You must do this by hand. $g(t) = egin{cases} 3, & 0 le t < 5; \ 10, & 5 le t le 8 \ 0, & t ge 8. end{cases}$ 2. Use Laplace transformation to solve the following differential equations. Make sure to show all the steps. In particular, you must show all the steps (including partial fraction and/or completing square) when finding inverse Laplace transformation. If you use computer for this, you will receive no credit. Refer to the number in the Laplace table that you are using. y'' - y = g(t), y(0) = 0 and y'(0) = 0 Here g(t) is the same as problem #1. So you can use your results from problem #1. You do not need to repeat that part.

          1. Find the Laplace Transformation of the following function. First express the function in
terms of $u_c(t)$. Then use #12 from the Laplace table. Do not use computer. You must do
this by hand.
$g(t) = egin{cases} 3, & 0 le t < 5; \ 10, & 5 le t le 8 \ 0, & t ge 8. end{cases}$
2. Use Laplace transformation to solve the following differential equations. Make sure to
show all the steps. In particular, you must show all the steps (including partial fraction
and/or completing square) when finding inverse Laplace transformation. If you use
computer for this, you will receive no credit. Refer to the number in the Laplace table that
you are using.
y'' - y = g(t), y(0) = 0 and y'(0) = 0
Here g(t) is the same as problem #1. So you can use your results from problem #1. You
do not need to repeat that part.

$1. Find the Laplace Transformation of the following function. First express the function in terms of uc(t). Then use #12 from the Laplace table. Do not use computer. You must do this by hand. g(t) = egincases 3, 0 le t < 5; 10, 5 le t le 8 0, t ge 8. endcases 2. Use Laplace transformation to solve the following differential equations. Make sure to show all the steps. In particular, you must show all the steps (including partial fraction and/or completing square) when finding inverse Laplace transformation. If you use computer for this, you will receive no credit. Refer to the number in the Laplace table that you are using. y” - y = g(t), y(0) = 0 and y'(0) = 0 Here g(t) is the same as problem #1. So you can use your results from problem #1. You do not need to repeat that part.$

Added by Tommy G.

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