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Find the Laplace transform of the function f (t) = 3t^4 – 2t^3 + 4e^-3t – 2sin5t + 3cos2t.(a) 72/s^5 – 12/s^4 + 4/(s+3)+10/(s^2+25)+3s/(s^2+4)(b) 72/s^5 – 12/s^4 + 4/(s+3)-10/(s^2+25)+3s/(s^2+4)(c) 72/s^5 – 12/s^4 – 4/(s+3)+10/(s^2+25)+3s/(s^2+4)(d) 72/s^5 – 12/s^4 – 4/(s+3)-10/(s^2+25)+3s/(s^2+4)I had been asked this question during an online exam.My doubt stems from Operational Transforms topic in portion Intoduction to the Laplace Transform of Network Theory

Answer»

Right answer is (b) 72/s^5 – 12/s^4 + 4/(s+3)-10/(s^2+25)+3s/(s^2+4)

Best explanation: L (3t^4 -2t^3+4e^-3t – 2sin5t +3cos2t) = 3 L (t^4)-2L (t^3)+4L (e^-3t)-2L (sin5t) + 3L (cos2t) = 72/s^5) -12/s^4 +4/(s+3)-10/(s^2+25)+3s/(s^2+4).



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