Q2/ a- Find the Laplace transform of the function illustrated in Fig.1. b- Find the Laplace transform of the first derivative of the function illustrated in Fig. 1. c- Find the Laplace transform of the second derivative of the function illustrated in Fig.1. f(t) 15 7.5 15 15-

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1. Laplace transform and its inverse -5t te a) Consider f(t) = To 05 70(1-7) i) Write f(t) in terms of step functions and t. ii) Find Laplace transform of f(t). 8.s 4s² + 12s+25 b) i) Find time domain function f(t) for the s-domain function F(s)=- ii) Find time domain function ƒ₁(†) for the s-domain function F₁(s) = e¯²³F(s).

For the given circuit R1= 40, R2= 30, L1= 5H, L2= 2H. Using inverse laplace transform, calculate H(t) for t= 0.2s where H(s)=Vo(s) / Is(s). L1 ll R1 R2 Is V.SL2 Remark1: Only numeric values must be entered. Do not enter the units. Remark2: Use maximum one digit after dot. Round the numbers as provided below. (ex: If you calculate 10.83 , write 10.8, not 11) (ex: if you calculate 15.67 , write 15.7, not 16) (ex: if you calculate 18.98 , write 19) Remark3: Don't use comma (ex: Write 50.6, not 50,6)