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The picture I have shared below shows the laplace transform of the circuit. The calculations shown are really simplified. I know how to do laplace transforms but the problem is they are super long and gets confusing after sometime. For example the equation I've marked with a blue star is really simplified but when I try to solve it, it gets really long and confusing. I've tried using my calculator (Casio fx-991EX Classwiz) for it but I can't seem to use anything instead of the letter s (for s-domain). I would really appreciate it if someone could tell me a simple and less confusing way to do laplace transforms. Maybe even show me how to use my calculator for it because I can't find any sources for laplace transformation done with my calculator. Thank you in advance.enter image description here

Edit: My attempt at solving was to just multiply everything and try to simplify them, but I noticed it was becoming a long equation.

enter image description here

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    \$\begingroup\$ Could you please show how you tried to solve the equation denoted by the blue asterisk? Otherwise, it'll be very hard to help you. \$\endgroup\$
    – uriyabsc
    Commented Jun 17, 2021 at 11:41
  • \$\begingroup\$ It's an university exercise, so I doubt you can use a calculator. At least when I was a student it was forbidden. I do suspect that any other form of the result is not valid, so keep doing the math exercise and forget about computer and calculator. \$\endgroup\$
    – Marko Buršič
    Commented Jun 17, 2021 at 11:41
  • \$\begingroup\$ @uriyaba I've added my attempt at solving. It doesn't show the whole solution because it was getting super long but my thought was to just do all the multiplication and just simplifying it. \$\endgroup\$
    – Kalamakra
    Commented Jun 17, 2021 at 12:00
  • \$\begingroup\$ @MarkoBuršič we can't use programmable calculators but the calculator I am using is allowed. So, if I can figure out a way to just find an alternative instead of the letter 's', I can easily solve them. I've tried using 'x' instead of 's' but it just does the calculation as if it is a variable, not as a place holder. \$\endgroup\$
    – Kalamakra
    Commented Jun 17, 2021 at 12:03

1 Answer 1

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You need to learn about solving partial fractions. That is what the K1, K2 and K3 formula is hinting at. If you haven't studied partial fractions then, it's going to be real tricky to split the equation that has the denominator s(s+8000)(s+20000) into three fractions that are added together as per the K1, K2 and K3 equation.

Go and study partial fractions is my recommendation. However, there is a math site that does solve PFs for you and comes up with this answer when converting \$\dfrac{1}{x(x+8000)(x+20000)}\$: -

$$\frac{1}{160000000x}-\frac{1}{96000000\left(x+8000\right)}+\frac{1}{240000000\left(x+20000\right)}$$

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    \$\begingroup\$ I've just realized what I was doing wrong. I don't have to multiply everything, like you said I just need to solve the partial fractions. Thank you for making me realize it. \$\endgroup\$
    – Kalamakra
    Commented Jun 17, 2021 at 12:25
  • \$\begingroup\$ No problemo @Kalamakra \$\endgroup\$
    – Andy aka
    Commented Jun 17, 2021 at 15:00
  • \$\begingroup\$ You can get a head start on the expansion by inspection of the circuit. K1 must = 90, because that's what Vo will end up at. K2 + K3 must = 60 because Vo starts at 150. \$\endgroup\$
    – john
    Commented Jun 19, 2021 at 14:32

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