Initially, there is no current in an RLC circuit with R = 20 Q,L=1 H and C = 0.001 F, and no charge on the capacitor. The circuit is connected to a battery supplying e(t) = 949 e 3t v. At time t= 0 the switch is closed and left closed for 3 seconds. At time t = 3 the switch is opened and left open thereafter. Find the resulting current in the circuit by solving the differential equation: di +Ri+ dt 1 i(x) dx = e(t).

Q: xn-1 ax

A:

Q: 5s2-4s-7 7. (s-3)(s²+4)

A:

Q: Find the laplace transform of (b) L-- [tan-" )]

A:

Q: be separated into additive components before undergoing Laplace Transformation. The Laplace…

A:

Q: 8) e* as4t

A:

Q: Evaluate the inverse laplace transform: F(s)=4s-2/s^2-6s+18

A:

Q: Determine the Laplace Transform of sin³3t

A:

Q: 6, 6 01 2 Lt

A:

Q: 3. State and explain the Convolution Theorem for Laplace transform

A: To prove: State and explain the convolution theorem for Laplace transform.

Q: L{ sin2(t-1) cos3rdt}

A:

Q: what is the discrete fourier transform of y = 001010

A: Introduction: Discrete Fourier transformation is applied when the signal is discrete and finite. For…

Q: f(x) = 0 if -1<x otherwi

A: Formula for the Fourier Transform of fx is  Fw=∫-∞∞fxeiwxdx We are given fx=|x|if…

Q: Determine the transform of the following functions using any methods . t^2 sinh 3t

A: According to the definition, the transform of the function f(t),  is given by L[f(t)]=∫0∞e-stf(t)dt,…

Q: FIND INVERSE LAPLACE TRANSFORM, USE THE LAPLACE OF INTEGRALS -7 7. SS+ 2. s+)

A:

Q: F(@) = ? -1 f(t) 1

A:

Q: Determine the Laplace transform of the functions shown and simplify . 23t^2 - 4e^2t

A: Some Laplace formulas: L(t2)=2s3 Leat=1s-a

Q: COST dr

A:

Q: find the Laplace transform of cos3tcos5t

A: In this question, we use the trigonometric identity and then properties of Laplace transform. L…

Q: * - 10x + 9x = 5t, x(0) = -1, x(0) = 2

A:

Q: 3-76SH

A:

Q: What are Practical uses of laplace transform in th efieldof engineering

A:

Q: Find the inverse Laplace Transform F(s)= 2s-6/s^2+9

A: We have to find the inverse Laplace transform of .Now, consider Apply the inverse Laplace transform,…

Q: -St Find aG 2t? t te

A: As per the instruction, we will answer only the first one. So,…

Q: Determine the Laplace transform of a.) 2cos^2 t and b.) 3sin^2 2x. Write the complete solution…

A:

Q: Laplace Transform

A: