Program Description: Purpose of the problem is to show that current in the R L C circuit is defined by the differential equation i ″ + 60 i ′ + 1000 i = 10 ∑ n = 0 ∞ ( − 1 ) n δ ( t − n π 10 ) ; i ( 0 ) = i ′ ( 0 ) = 0 .

Question

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Answer 1

Question

Chapter 7.6, Problem 21P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that current in the RLC circuit is defined by the differential equation i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to solve the differential equation

i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 and show i(t)=e3nπ+3π−1e3π−1e−30tsin10t if nπ10<t<(n+1)π10 .

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2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…

Electromagnetic Pulse propagating at oblique angle to a dielectric interface Consider a gaussian wave pulse propagating along the z-axis from region 1 with refractive index n1 and onto a dielectric interface y = m z (for all x). To the left of this dielectric interface, the refractive index is n2. Devise an initial value computer algorithm to determine the time evolution of the reflected and transmitted electromagnetic fields for this pulse. e.g., n1 = 1 , n2 = 2 initial profile (t = 0, with z0 < 0) Ex = E0 exp[-a (z-z0)^2] By = n1 * Ex Choose parameters so that the pulse width is at least a fact of 8 less than the z- domain of integration ( -L < z < L). For the slope of the interface, one could choose m = 1.

3. You have seen how Kirchhoff's laws were used in your lectures to obtain a 2nd order differential equation where we solved for the current. This time we will use an even simpler concept: principle of conservation of energy to derive the 2nd order differential equation where we will solve for the charge. Take a look at the circuit below. IHE 2F In the circuit above, we have a capacitor with capacitance 2 F, an inductor of inductance 5 H and a resistor of 32 (a) The total energy that is supplied to the resistor is LI? E = 2 Q? 20 where L is the inductance, I is the current, C is the capacitance and Q is the charge. Write down the total energy supplied E in terms of Q and t only. OP Remember that I = dt (b) Now you know that the power dissipation through a resistor is -1R. Use the conservation of energy (energy gain rate = energy loss rate) to derive the differential equation in terms Q and t only. (c) Solve the differential equation for initial charge to be Qo with a initial current of…

Answer 2

Question

Chapter 7.6, Problem 21P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that current in the RLC circuit is defined by the differential equation i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to solve the differential equation

i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 and show i(t)=e3nπ+3π−1e3π−1e−30tsin10t if nπ10<t<(n+1)π10 .

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See solution

Answer 3

Question

Chapter 7.6, Problem 21P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that current in the RLC circuit is defined by the differential equation i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to solve the differential equation

i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 and show i(t)=e3nπ+3π−1e3π−1e−30tsin10t if nπ10<t<(n+1)π10 .

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 7.6, Problem 21P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that current in the RLC circuit is defined by the differential equation i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to solve the differential equation

i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 and show i(t)=e3nπ+3π−1e3π−1e−30tsin10t if nπ10<t<(n+1)π10 .

Expert Solution & Answer

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Answer 5

Chapter 7.6, Problem 21P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that current in the RLC circuit is defined by the differential equation i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to solve the differential equation

i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 and show i(t)=e3nπ+3π−1e3π−1e−30tsin10t if nπ10<t<(n+1)π10 .

Answer 6

Chapter 7.6, Problem 21P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that current in the RLC circuit is defined by the differential equation i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 .

Answer 7

Chapter 7.6, Problem 21P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that current in the RLC circuit is defined by the differential equation i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 .

Answer 8

(b)

Program Plan Intro

Program Description: Purpose of the problem is to solve the differential equation

i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 and show i(t)=e3nπ+3π−1e3π−1e−30tsin10t if nπ10<t<(n+1)π10 .

Answer 9

(b)

Program Plan Intro

Program Description: Purpose of the problem is to solve the differential equation

i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 and show i(t)=e3nπ+3π−1e3π−1e−30tsin10t if nπ10<t<(n+1)π10 .

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

Program Description: Purpose of the problem is to show that current in the R L C circuit is defined by the differential equation i ″ + 60 i ′ + 1000 i = 10 ∑ n = 0 ∞ ( − 1 ) n δ ( t − n π 10 ) ; i ( 0 ) = i ′ ( 0 ) = 0 .

Solution Summary: The author explains that current in the RLC circuit is defined by the differential equation e_0 battery voltage.

Concept explainers

Program Description: Purpose of the problem is to show that current in the RLC circuit is defined by the differential equation i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 .

Program Description: Purpose of the problem is to solve the differential equation

i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 and show i(t)=e3nπ+3π−1e3π−1e−30tsin10t if nπ10<t<(n+1)π10 .

Want to see the full answer?

Chapter 7 Solutions

Program Description: Purpose of the problem is to show that current in the R L C circuit is defined by the differential equation i ″ + 60 i ′ + 1000 i = 10 ∑ n = 0 ∞ ( − 1 ) n δ ( t − n π 10 ) ; i ( 0 ) = i ′ ( 0 ) = 0 .

Solution Summary: The author explains that current in the RLC circuit is defined by the differential equation e_0 battery voltage.

Concept explainers

Program Description: Purpose of the problem is to show that current in the RLC circuit is defined by the differential equation i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 .

Program Description: Purpose of the problem is to solve the differential equation i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 and show i(t)=e3nπ+3π−1e3π−1e−30tsin10t if nπ10<t<(n+1)π10 .

Want to see the full answer?

Chapter 7 Solutions

Program Description: Purpose of the problem is to solve the differential equation

i″+60i′+1000i=10∑n=0∞( −1)nδ(t− nπ 10);i(0)=i′(0)=0 and show i(t)=e3nπ+3π−1e3π−1e−30tsin10t if nπ10<t<(n+1)π10 .