Find the convolution results between f(t) and x(t): 1) Use graphical method. 2) Use Laplace Transform to validate your result in 1). f(t) 15 6 凹 x₁(t) 1 0 1 2 3_4t 0 1t

Using the Laplace transform, find the current i(t) in the circuit in the figure with R= 102 and C= 10-2F, where the current at t = 0 is assumed to be zero, and: v = 0 if t 3. i(t) = i(t) = с if t 3 www R

Find Laplace transform for x(t) in the following differential equations assuming zero initialconditions 12dx(t)/dt2 + 31dx(t)/dt+ 23x(t) = 1215d3x(t)dt3 + 13dx(t)dt= 31

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