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  3. q1 compute the laplace transforms of the following functions use...

Question: q1 compute the laplace transforms of the following functions use...

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Q1 Compute the Laplace transforms of the following functions. Use Tables 1 and 2 to perform your caleulations, if desired. Verify your answer using MATLABs laplace function. (i) /(1)-sin(at +d) (ii) Consider the function shown in Figure 1 with 0 a < b. Table of Laplace Trannslorms Number F Properties of Laplace Transforms Number Laplace Transform Time Function Comment Transform pair Superposition Time delay ( 0) Time scaling Shift in frequency 10e) Fis) 3 1/ afi(11+ßftr) ft-A) (at) Figure 1: Q1, Part ii) F(s) f0dζ Integration iii) From lecture we know lhal sufficient conditions for a Lap ace Trans orm of雥function U1) to 1, FiG)F2(s) lim sF(s) )5t) Convolution exist are (a) the function f() is piecewise continuous on the interval [0, oo) (b) the function(t) has erponential order, e, tee exists M, a, T E R such that Initial Value Theorem Final Value Theorem im F) lim fa) 10 Time product Does the function ()/V satisfy the above suficient conditions? Can you compute its transform an du V/2. Laplace transform? Hint: use the u st variable substitution in the definition of the Laplace 16- m . 酐 12 F(s) fa) Multiplication by time Note: to simplify a symbolic expression in MATLAB use simplify and to display it nicely use pretty. For exarnple, suppose we consider a delayed unit step function f(t) 1(1-a),a > 0, Then the MATLAB code for its Laplace ransform is 18 coa Table 1: Properties of Laplace Transform from Franklin (Table A.1) 19 syms t; syms a positive;pretty(simplify(laplace(heaviside(t-a)))) which returns exp (-a s) Tse 2: Laplace Tudorme um Franklin (Tabk A

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