Plot the one full cycle of the periodic function over the interval − T / 4 ≤ t ≤ 3 T / 4 .

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Answer 1

Question

Chapter 16, Problem 14P

a.

To determine

Plot the one full cycle of the periodic function over the interval −T/4≤t≤3T/4.

b.

To determine

Derive the expressions for the Fourier coefficients av,ak, and bk.

c.

To determine

Derive the first three nonzero terms in the Fourier series of f(t).

d.

To determine

Calculate the value of f(T/8) using first three nonzero terms in the Fourier series.

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Given the following reaction system, where Xo is the input, i.e u(t) = k₁ × Xo: $Xo -> x1; k1*Xo x2; k2*x1 x1 2 x2 ->%; k3*x2^2 x2 ->; k4*x2 Xo 1; k1 = 0.4 k2 4.5; k3 = 0.75 k4= 0.2 a) Build the model in Tellurium and run a simulation. Compute the Jacobian at steady state using the method getFull Jacobian(). Make sure you are at steady state! b) Write out the values for n and p c) Write out the differential equations. d) Write out the state space representation in terms of the rate constants etc. e) Compute the values in the Jacobian matrix from d) by substituting the values of the rate constants etc and any data you need from the simulation. f) Confirm that the Jacobian you get in e) is the same as the one computed from the simulation in a). g) Is the system stable or not? If you find an eigenvalue of zero, that means the system is marginally stable. You can get the eigenvalues using the tellurium method r.getFullEigenvalues()

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Answer 2

Question

Chapter 16, Problem 14P

a.

To determine

Plot the one full cycle of the periodic function over the interval −T/4≤t≤3T/4.

b.

To determine

Derive the expressions for the Fourier coefficients av,ak, and bk.

c.

To determine

Derive the first three nonzero terms in the Fourier series of f(t).

d.

To determine

Calculate the value of f(T/8) using first three nonzero terms in the Fourier series.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 16, Problem 14P

a.

To determine

Plot the one full cycle of the periodic function over the interval −T/4≤t≤3T/4.

b.

To determine

Derive the expressions for the Fourier coefficients av,ak, and bk.

c.

To determine

Derive the first three nonzero terms in the Fourier series of f(t).

d.

To determine

Calculate the value of f(T/8) using first three nonzero terms in the Fourier series.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 16, Problem 14P

a.

To determine

Plot the one full cycle of the periodic function over the interval −T/4≤t≤3T/4.

b.

To determine

Derive the expressions for the Fourier coefficients av,ak, and bk.

c.

To determine

Derive the first three nonzero terms in the Fourier series of f(t).

d.

To determine

Calculate the value of f(T/8) using first three nonzero terms in the Fourier series.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 16, Problem 14P

a.

To determine

Plot the one full cycle of the periodic function over the interval −T/4≤t≤3T/4.

b.

To determine

Derive the expressions for the Fourier coefficients av,ak, and bk.

c.

To determine

Derive the first three nonzero terms in the Fourier series of f(t).

d.

To determine

Calculate the value of f(T/8) using first three nonzero terms in the Fourier series.

Answer 6

Chapter 16, Problem 14P

a.

To determine

Plot the one full cycle of the periodic function over the interval −T/4≤t≤3T/4.

Answer 7

Chapter 16, Problem 14P

a.

To determine

Plot the one full cycle of the periodic function over the interval −T/4≤t≤3T/4.

Answer 8

b.

To determine

Derive the expressions for the Fourier coefficients av,ak, and bk.

Answer 9

b.

To determine

Derive the expressions for the Fourier coefficients av,ak, and bk.

Answer 10

c.

To determine

Derive the first three nonzero terms in the Fourier series of f(t).

Answer 11

c.

To determine

Derive the first three nonzero terms in the Fourier series of f(t).

Answer 12

d.

To determine

Calculate the value of f(T/8) using first three nonzero terms in the Fourier series.

Answer 13

d.

To determine

Calculate the value of f(T/8) using first three nonzero terms in the Fourier series.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 16.2 - Objective 1–Be able to calculate the trigonometric...Ch. 16.2 - Prob. 2AP Ch. 16.3 - Derive the Fourier series for the periodic voltage...Ch. 16.4 - Compute A1 – A5 and θ1 – θ5 for the periodic...Ch. 16.5 - The periodic triangular-wave voltage seen on the...Ch. 16.5 - The periodic square-wave shown on the top is...Ch. 16.6 - a. 16.7 The periodic voltage function in...Ch. 16.8 - Derive the expression for the Fourier coefficients...Ch. 16.8 - Calculate the rms value of the periodic current in...Ch. 16.9 - Prob. 10AP

Plot the one full cycle of the periodic function over the interval − T / 4 ≤ t ≤ 3 T / 4 .

Plot the one full cycle of the periodic function over the interval −T/4≤t≤3T/4.

Derive the expressions for the Fourier coefficients av,ak, and bk.

Derive the first three nonzero terms in the Fourier series of f(t).

Calculate the value of f(T/8) using first three nonzero terms in the Fourier series.

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Chapter 16 Solutions