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Laplace Transform Theories

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  • 1. Multiple Choice
    30 seconds
    1 pt

    Given  g(t)=e5tf(t)g\left(t\right)=e^{5t}f\left(t\right)  , what is G(s)?

     G(s)=F(s5)G\left(s\right)=F\left(s-5\right)  

     G(s)=(1)5d5F(s)ds5G\left(s\right)=\left(-1\right)^5\frac{\text{d}^5F\left(s\right)}{\text{d}s^5}  

     G(s)=F(s+5)G\left(s\right)=F\left(s+5\right)  

     G(s)=(1)4d4F(s)ds4G\left(s\right)=\left(-1\right)^4\frac{\text{d}^4F\left(s\right)}{\text{d}s^4}  

  • 2. Multiple Choice
    30 seconds
    1 pt

    Given  g(t)=t3f(t)g\left(t\right)=t^3f\left(t\right)  , what is G(s)?

     G(s)=F(s3)G\left(s\right)=F\left(s-3\right)  

     G(s)=(1)3d3F(s)ds3G\left(s\right)=\left(-1\right)^3\frac{\text{d}^3F\left(s\right)}{\text{d}s^3}  

     G(s)=F(s+3)G\left(s\right)=F\left(s+3\right)  

     G(s)=(1)2d2F(s)ds2G\left(s\right)=\left(-1\right)^2\frac{\text{d}^2F\left(s\right)}{\text{d}s^2}  

  • 3. Multiple Choice
    30 seconds
    1 pt

    Given  g(t)=f(t)tg\left(t\right)=\frac{f\left(t\right)}{t}  , what is G(s)?

     G(s)=sF(u)duG\left(s\right)=\int_s^{\infty}F\left(u\right)du  

     G(s)=(1)dF(s)dsG\left(s\right)=\left(-1\right)\frac{\text{d}F\left(s\right)}{\text{d}s}  

     G(s)=sF(u)duG\left(s\right)=\int_{\infty}^sF\left(u\right)du  

     G(s)=(1)1dF(s)dsG\left(s\right)=^{\left(-1\right)^{-1}}\frac{\text{d}F\left(s\right)}{\text{d}s}  

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