Explanation Given data: Refer to Figure 15.33 in the textbook for f ( t ) . Formula used: Write the general expression to find the Laplace transform function. L [ u ( t ) ] = 1 s (1) L [ t ] = 1 s 2 (2) Here, s is a complex variable. Write the general expression for using time shift property. L [ f ( t − a ) u ( t − a ) ] = e − a s F ( s ) (3) Here, e − a s is the time-delay or time-shift property. Write the general expression for using time periodicity. F ( s ) = F 1 ( s ) 1 − e − s T (4) Here, F 1 ( s ) is the Laplace transform of f ( t ) defined over its first period only, T is the period of the waveform. Calculation: From Figure 15.31, the period of waveform is T = 2 π and the expression for periodic waveform f ( t ) can be written as, f ( t ) = ( 1 − t 2 π ) [ u ( t ) − u ( t − 2 π ) ] f ( t ) = u ( t ) − t 2 π u ( t ) + 1 2 π ( t − 2 π ) u ( t − 2 π ) (5) F 1 ( s ) is the Laplace transform of f ( t ) defined over its first period and it is calculated by applying the time shift property in equation (3) and Laplace transform function given in equation (1) and (2) to equation (5)

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Chapter 15, Problem 21P

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Calculate the Laplace transform of the periodic waveform f(t) in the given Figure 15.33.

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Chapter 15, Problem 20P

Chapter 15, Problem 22P

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Q2/ Skitch the following aperiodic waveform in the time domain and calculate it is Fourier transform. - 22t3 2 %3D otherwise %3D

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Solve a problem showing the application of Laplace transforms in the field of electrical engineering. The problem should be in circuit analysis, transient analysis, control systems, power systems, or other subfields of EE.

Chapter 15 Solutions

Fundamentals of Electric Circuits

Ch. 15.2 - Prob. 1PP Ch. 15.2 - Prob. 2PP Ch. 15.3 - Prob. 3PP Ch. 15.3 - Prob. 4PP Ch. 15.3 - Prob. 5PP Ch. 15.3 - Prob. 6PP Ch. 15.3 - Obtain the initial and the final values of...Ch. 15.4 - Prob. 8PP Ch. 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. 15PP Ch. 15.6 - Prob. 16PP Ch. 15 - Prob. 1RQ Ch. 15 - Prob. 2RQ Ch. 15 - Prob. 3RQ Ch. 15 - Prob. 4RQ Ch. 15 - Prob. 5RQ Ch. 15 - If F(s) = 1/(s + 2), then f(t) is (a) e2t u(t) (b)...Ch. 15 - Prob. 7RQ Ch. 15 - Prob. 8RQ Ch. 15 - Prob. 9RQ Ch. 15 - Prob. 10RQ Ch. 15 - Prob. 1P Ch. 15 - Prob. 2P Ch. 15 - Prob. 3P Ch. 15 - Prob. 4P Ch. 15 - Prob. 5P Ch. 15 - Prob. 6P Ch. 15 - Prob. 7P Ch. 15 - Prob. 8P Ch. 15 - Prob. 9P Ch. 15 - Prob. 10P Ch. 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. 13P Ch. 15 - Prob. 14P Ch. 15 - Prob. 15P Ch. 15 - Prob. 16P Ch. 15 - Prob. 17P Ch. 15 - Prob. 18P Ch. 15 - Prob. 19P Ch. 15 - Prob. 20P Ch. 15 - Prob. 21P Ch. 15 - Prob. 22P Ch. 15 - Prob. 23P Ch. 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. 27P Ch. 15 - Prob. 28P Ch. 15 - Prob. 29P Ch. 15 - Prob. 30P Ch. 15 - Find f(t) for each F(s): (a) 10ss+1s+2s+3 (b)...Ch. 15 - Prob. 32P Ch. 15 - Prob. 33P Ch. 15 - Prob. 34P Ch. 15 - Obtain f(t) for the following transforms: (a)...Ch. 15 - Prob. 36P Ch. 15 - Prob. 37P Ch. 15 - Prob. 38P Ch. 15 - Determine f(t) if: (a)...Ch. 15 - Show that...Ch. 15 - Prob. 41P Ch. 15 - Design a problem to help other students better...Ch. 15 - Prob. 43P Ch. 15 - Prob. 44P Ch. 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. 49P Ch. 15 - Prob. 50P Ch. 15 - Given that v(0) = 5 and dv(0)/dt = 10, solve...Ch. 15 - Prob. 52P Ch. 15 - Prob. 53P Ch. 15 - Design a problem to help other students better...Ch. 15 - Prob. 55P Ch. 15 - Solve for v(t) in the integrodifferential equation...Ch. 15 - Prob. 57P Ch. 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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