Quiz about Mr Ng's MA1512 Championship - Round 4

Question 1

What is the Laplace transform of a function $$f\left(t\right)$$ ?

Accepted Answer

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

Answer

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

Answer

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

Answer

$$F\left(s\right)=\int_{-\infty}^{\infty}f\left(t\right)dt$$

Question 2

Given two functions $$f\left(t\right)$$ and $$g\left(t\right)$$ with their respective Laplace transforms $$F\left(s\right)$$ and $$G\left(s\right)$$ , what is the inverse Laplace transform of the linear combination $$2F\left(s\right)-3G\left(s\right)$$ ?

Accepted Answer

$$2f\left(t\right)-3g\left(t\right)$$

Answer

$$2f\left(t\right)+3g\left(t\right)$$

Answer

$$f\left(2t\right)-g\left(3t\right)$$

Answer

$$f\left(2t\right)+g\left(3t\right)$$

Question 3

Identify the Laplace transforms that involve the First Shifting Theorem.

Accepted Answer

$$L\left(e^{2t}\right)$$

Accepted Answer

$$L\left(e^{5t}\sin\left(t\right)\right)$$

Answer

$$L\left(t^3\right)$$

Answer

$$L\left(\cos\left(4t\right)\right)$$

Question 4

Accepted Answer

impulses or point charges

Answer

continuous waveforms

Answer

discrete waveforms

Answer

complex functions

Question 5

Accepted Answer

$$e^{-sc}F\left(s\right)$$

Answer

$$F\left(s-c\right)$$

Answer

$$e^{sc}F\left(s\right)$$

Answer

$$F\left(s+c\right)$$