1. Convert the following functions of time (defined for t20) to functions of s using Laplace Transforms: a) f(t)= et sin

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1 Convert The Following Functions Of Time Defined For T20 To Functions Of S Using Laplace Transforms A F T Et Sin 1 (44.33 KiB) Viewed 37 times

1. Convert the following functions of time (defined for t20) to functions of s using Laplace Transforms: a) f(t)= et sin (27) b) f(t)=3e²+7e-4 +1² 2. Find 2-¹ {F(s)} when F(s) is given by the following expression: 28 +6 8² +4 3. Using Laplace transform methods, a) solve for t≥ 0 the following conditions: differential equation, subject to the specified initial da +3x=2; (0) = 2 (7 marks) dt b) Show all the properties applied to solve the differential equation above. (4 marks) 5. Find the Fourier transform of the following functions: a) f(t) = ps(3t) b) f(t)= 4. Show that the functions Bo(r) = 1 and B₁(x) = √3(1-2r) are orthonormal with respect to the inner product (1.9) = f(x)g(x)dx. (9 marks) 19, 2≤t≤6 10. Otherwise 6. Let f(r) cosh(z) and a = 2. backward and central differences. with the exact result which is sinh(2). 7. An experiment is carried out and the following data obtained: (3 marks) (3 marks) (6 marks) In 0.24 0.26 0.28 0.30 fn 1.25 0.80 0.50 0.20 Let h = 0.01 and approximate f'(a) using forward, Work to 8 decimal places and compare your answers (9 marks) Use linear regression to fit the given dataset. (2 marks) (2 marks) (10 marks)