1. Find the Laplace transform of the given function, f(t) = 3t^2 e^-2t 2. Find t
ID: 2833436 • Letter: 1
Question
1. Find the Laplace transform of the given function, f(t) = 3t^2 e^-2t
2. Find the inverse transform of the given function, F(s) = 2/ S^3-12S^2+48S-64
3. Express the transform of the given expresion in term of S and L(f), 4y'' + y' + 2y, f(0) = 0, f'(0) = -1
4. A 10-H indicator, a 40-uF capacitor and a voltage supply whose voltage is given by electric circuit. Find the current as a factor of the time if the initial charge on the capacitot is zero and initial current is zero.
5. Solve the given differential equation by Laplace transform. The function is subject to the given condition,
y'' - 8y' + 32 =0, y(0)=-1, y'(0)=-4
Explanation / Answer
1)
L{e^(-2t)} = 1/[s + 2]
L{t e^(-2t)} = 1/(s+2)^2
L{t^2 e^(-2t)} = 2/(s - 2)^3
F(s) = L{t^2 e^(-2t)} = 2/(s - 2)^3
2)
F(s) = 2/ S^3-12S^2+48S-64 = 2/(s - 4)^3
f(t) = L^-1{F(s)} = t^2 * e^(4t)
3)
L{4y'' + y' + 2y} = 4s^2 L{f} - 4sf(0) - 4f'(0) + sL{f} - f(0) + 2L{f}
= 4s^2L{f} + 4 + sL{f} + 2L{f}
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