Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
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Chapter 15.2, Problem 1PP
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Calculate the Laplace transform for the given functions
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Problem 2. Which gives the Laplace transforms of the given time-domain function?
-2.5 ln [(s+1)(s+4)]
-2.5 ln [(s-1)/(s-4)]
-2.5 ln [(s+1)/(s+4)]
-2.5 ln [(s+4)/(s+1)]
1. Find the Laplace transform of the given functions, where a and b are constants
a) eat sinh bt
b) eat cosh bt
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1. By the direct integration, i.e. using the formula of Laplace transform, find the Laplace transform of (i) 2u(t) − 2u(t − 1), (ii) te^−(2t)u(t).2. Also, state their region of convergence. 3. Sketch both of the signals.
Chapter 15 Solutions
Fundamentals of Electric Circuits
Ch. 15.2 - Prob. 1PPCh. 15.2 - Prob. 2PPCh. 15.3 - Prob. 3PPCh. 15.3 - Prob. 4PPCh. 15.3 - Prob. 5PPCh. 15.3 - Prob. 6PPCh. 15.3 - Obtain the initial and the final values of...Ch. 15.4 - Prob. 8PPCh. 15.4 - Find f(t) if F(s)=48(s+2)(s+1)(s+3)(s+4)Ch. 15.4 - Obtain g(t) if G(s)=s3+2s+6s(s+1)2(s+3)
Ch. 15.4 - Find g(t) given that G(s)=20(s+1)(s2+4s+13)Ch. 15.5 - Graphically convolve the two functions in Fig....Ch. 15.5 - Given g(t) and f(t) in Fig. 15.20, graphically...Ch. 15.5 - Use convolution to find vo(t) in the circuit of...Ch. 15.6 - Prob. 15PPCh. 15.6 - Prob. 16PPCh. 15 - Prob. 1RQCh. 15 - Prob. 2RQCh. 15 - Prob. 3RQCh. 15 - Prob. 4RQCh. 15 - Prob. 5RQCh. 15 - If F(s) = 1/(s + 2), then f(t) is (a) e2t u(t) (b)...Ch. 15 - Prob. 7RQCh. 15 - Prob. 8RQCh. 15 - Prob. 9RQCh. 15 - Prob. 10RQCh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Find F(s) if: (a) ft=6etcosh2t (b) ft=3te2tsinh4t...Ch. 15 - If g(t) = 4e 2t cos 4t, find G(s).Ch. 15 - Prob. 13PCh. 15 - Prob. 14PCh. 15 - Prob. 15PCh. 15 - Prob. 16PCh. 15 - Prob. 17PCh. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - Prob. 20PCh. 15 - Prob. 21PCh. 15 - Prob. 22PCh. 15 - Prob. 23PCh. 15 - Design a problem to help other students better...Ch. 15 - Let F(s)=18(s+1)(s+2)(s+3) (a) Use the initial and...Ch. 15 - Determine the initial and final values of f(t), if...Ch. 15 - Prob. 27PCh. 15 - Prob. 28PCh. 15 - Prob. 29PCh. 15 - Prob. 30PCh. 15 - Find f(t) for each F(s): (a) 10ss+1s+2s+3 (b)...Ch. 15 - Prob. 32PCh. 15 - Prob. 33PCh. 15 - Prob. 34PCh. 15 - Obtain f(t) for the following transforms: (a)...Ch. 15 - Prob. 36PCh. 15 - Prob. 37PCh. 15 - Prob. 38PCh. 15 - Determine f(t) if: (a)...Ch. 15 - Show that...Ch. 15 - Prob. 41PCh. 15 - Design a problem to help other students better...Ch. 15 - Prob. 43PCh. 15 - Prob. 44PCh. 15 - Given h(t) = 4e2tu(t) and x(t) = (t) 2e 2tu(t),...Ch. 15 - Given the following functions...Ch. 15 - A system has the transfer function...Ch. 15 - Find f(t) using convolution given that: (a)...Ch. 15 - Prob. 49PCh. 15 - Prob. 50PCh. 15 - Given that v(0) = 5 and dv(0)/dt = 10, solve...Ch. 15 - Prob. 52PCh. 15 - Prob. 53PCh. 15 - Design a problem to help other students better...Ch. 15 - Prob. 55PCh. 15 - Solve for v(t) in the integrodifferential equation...Ch. 15 - Prob. 57PCh. 15 - Given that dvdt+2v+50tv()d=4u(t) with v(0) = 1,...Ch. 15 - Solve the integrodifferential equation...Ch. 15 - Prob. 60P
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- Explain (i) Derive the Laplace transforms of Step and Sine forcing function (ii) Determine f(t) for f(s) = 1/[s2 (s + 1)]arrow_forwardSuppose for the circuit shown, Idc=24 mA, R=625 Ω, L=25 mH, and C=25 nF. There is no energy stored in the circuit when the switch opens at t=0. 1. Find V(s), the Laplace transform of v(t). 2. Find v(t) by finding the inverse transform of the partial fraction expansion of V(s).arrow_forwardshow the derivation of the laplace transform for f (t) = sin wtarrow_forward
- Problem 5. Which gives the Laplace transforms of the given time-domain function? ln [(s + sqrt 2)/(s - sqrt 5)] ln [(s - sqrt 2)/(s + sqrt 5)] ln [(s - 2)/(s + 5)] ln [(s - sqrt 2)(s + sqrt 5)]arrow_forwardProblem 1. Which gives the Laplace transforms of the given time-domain function? Let a = 2 pi - 2arctan (s/6) pi - 2arctan (2s/3) pi - 2arctan (s/3) (1/2)pi - 2arctan (s/3)arrow_forwardFunction of x equals {2, zero<t<five} {0, five<t<ten} {e^4t, ten<t} What is the Laplace transform of the function of x above? N.b Kindly note the less than & greater signs very well.arrow_forward
- Find the inverse Laplace transform, f(t)of the function F(s)=(−2s+4)/(s^2+100) s>0t>0arrow_forwardThe dynamics of a system is derived from the inverse Laplace transform of X(s) = (s + 3) / (s)(s + 5) , determine the equation that defines X(t)?arrow_forwardFrom the first order system in the picture kv = 0.5 kp = 1.5 and ka = 4 using laplace transforms derive an expression to show how the output (angular displacement) will vary with time when a step input of 10v is appliedarrow_forward
- Derive the Laplace transform of the following function 1.cos btarrow_forwardFind the inverse Laplace transform, f(t) of the function F(s)=6s−32 s>0 t>0arrow_forwardFormulate and solve the 2nd order homogeneous differential equation for node voltage v(t). Given that the constant source current, resistor, capacitor and inductor are 10A, 12ohm, 6F and 64H, respectively. Use Laplace Transform to solve the differential having an initial condition, v’(0) = 1, v(0)=0.arrow_forward
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