3.1 Laplace Transform

Laplace Transform transforms a function from

• $f\left(t\right)\ to\ F\left(s\right)$

• $F\left(s\right)\ to\ f\left(t\right)$

• $f\left(t\right)\ to\ f'\left(t\right)$

• $f"\left(t\right)\ to\ f'\left(t\right)$

Tags

CCSS.HSF.IF.A.2

Which one is the correct definition of Laplace Transform?

• $F\left(s\right)=\int_0^{\infty}e^{-st}f\left(t\right)dt$

• $F\left(s\right)=\int_0^tf\left(t\right)g\left(t-u\right)$

What is the Laplace Transform for  $f\left(t\right)=t^3$  ?

•  $\frac{1}{s^3}$  

•  $\frac{2}{s^3}$  

•  $\frac{6}{s^4}$  

•  $\frac{3}{s^3}$  

What is Laplace Transform for $e^{-2t}$  ?

•  $\frac{1}{s-2}$  

•  $\frac{1}{s+2}$  

•  $\frac{2}{s}$  

•  $\frac{1}{s^2}$  

Tags

CCSS.HSF.LE.A.1

What is Laplace Transform for  $\sin\ 2t$  ?

•  $\frac{2}{s^2+2}$  

•  $\frac{s}{s^2+2}$  

•  $\frac{2}{s^2+4}$  

•  $\frac{s}{s^2+4}$  

What is Laplace Transform for  $6\ \sin\ 2t$  ?

•  $\frac{2}{s^2+4}$  

•  $\frac{s}{s^2+4}$  

•  $\frac{6}{s^2+4}$  

•  $\frac{12}{s^2+4}$  

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.3

Define this property:  $L\left(f\left(t\right)e^{at}\right)=F\left(s-a\right)$  

• Linearity Property

• First Shifting Property

• Convolution Theorem

• Second Shifting Property

 $L\left(e^{3t}t\right)$ Based on first shifting property, what is  $a$   value?

• 1

• 2

• 3

• 4

Find  $L\left(e^{3t}t\right)$  

•  $\frac{1}{\left(s^2\right)}$  

•  $\frac{1}{\left(s-3\right)^2}$  

•  $\frac{1}{\left(s-2\right)^2}$  

•  $\frac{1}{\left(s\right)}$  

Tags

CCSS.HSF.LE.A.1

 $L\left(e^{2t\ }\sin\ t\right)$  What is a and f(t)?

•  $a=2,\ f\left(t\right)=e^{2t}$  

•  $a=4,\ f\left(t\right)=\cos\ t$  

•  $a=2,\ f\left(t\right)=\sin\ t$  

Tags

CCSS.HSF.TF.B.5

CCSS.HSF.IF.A.2