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GENERAL PROBLEMS In Problems 5-1 through 5-18, determine the Laplace transforms of the functions givenus- ing...
1. Find the Laplace transforms of these functions: r(t) = tu(t), that is, the ramp function; Ae-atu(t); Be atu(t). 2. Determine the Laplace transform of f(t) = 50cos ot u(t). 3. Obtain the Laplace transform of f(t) = (cos (2t) + e 41) u(t). 4. Find the Laplace transform of u(t-2). 5. Find vo(t) in the circuit shown below, assuming zero initial conditions. IH F + 10u(i) 42 v. (1)
Only #23,27,33,41 step by step neatly please
In Problems 5-21 through 5-30, determine the inverse Laplace transforms of the functions given using Table 5-1 (and Table 5-2, if appropriate). 5-21 V(s) = 5+ 3 3 4 5-22 1(s) = 2 + + SS 5-23 32 F(S) = 2 + 64 SYE 6-24 10s 1(s) = 2 + 25 5-25 V(s) = Os + 15 8² +9 delta In Problems 5-31 through 5-48, determine the inverse transforms of the functions giv...
Homework Set 5 f(t) F(S) Section 4.1: Apply the definition to directly find the Laplace transforms of the given functions. (s > 0) 1 (s > 0) S- 1. Kt) = 12 2. f = 23t+1 Use transforms from the Table (op right) to find the Laplace transforms of the given functions. t" ( n20) (s > 0) r(a + 1) 1a (a > -1) (s > 0) 5+1 3. f(t) = VE +8t 4. f(t) = sin(2tcos(2t) Use the...
1) Laplace transforms/Transfer functions Use Laplace transform tables!!!! 1.1: Find the Laplace transform of f(t) = (cos(2t) + e-4t)-u(t) (simplify into one ratio)
For problems involving the Laplace transform, use the official table of Laplace transforms and label all properties, formula numbers and constants. For all problems on this assignment, you are not allowed to use any technology to arrive at your answers! 1. Evaluate the integral €2* cos(3t)8(t – 7) dt. 0
Find the Laplace transforms of the following functions:
a) f(t) = sin(at + b) Using the integral of the
Laplace transform
b) f(t) = cos(t) + sin(t/2) You can directly use
table 5.1
Tableau 5.1 Transformées de Laplace les plus couramment utilisées f(t)= £. {F()} F(s)= £{f(t)} f(t)=1 F(s) = 2 f(t)=1 F(s) == 2 3 Sl)=12 F(s) n! 4 St=1" F(s)=- 5 () at F(s)- S-a n! 6 S()=1"ar F($)= (s-a)"+1 a 7 s(t)= sin(at) F(s) s? +a? S...
Compute Laplace transforms of the following functions: (a) f1 = (1 + t) (b) f2 = eat sin(bt) 11, 0<t<1, (c) f3 = -1 1<t<2, | 2, t>2, Find the functions from their Laplace transforms: (a) Lyı] s(s + 1) (s +3) 2+s (b) L[42] = 52 + 2 s +5 (c) L[y3] = Solve the following initial value problems using the Laplace transform. Confirm each solution with a Matlab plot showing the function on the interval 0 <t<5. (a)...
2. Determine the Laplace transforms of the periodic functions in Fig. An 1 2 3 4 0 246 3. Determine the inverse Laplace transform of each of the following functions: (a) F(s)4+ (b) G(s) 3s+ H)+3) (d) J(s) = (s +2)2(s + 4) Find the inverse Laplace transform of: s s+1 s+4 4 12 4. s+13 s(S +4s
Fill in the table with the appropriate Laplace or inverse Laplace transforms. You may use the Laplace Transform table located on D2L in the same folder as this quiz. f(t) = C-'{F(*)} F(s) = {{f(t)} eU(t - 3) e-2 cosh(41) S- 2 $2 + 2s + 10
OF -1 One property of Laplace transforms can be expressed in terms of the inverse Laplace transform as I (1= - t) ft), wheref="{F). Use this equation to compute -'F) ds F(s) - arctan 18 5 Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms '9-0 Enter your answer in the answer box • Previous ch