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Differential Equations

Differential Equations

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Differential Equations
A series circuit has a capacitor of 0.25 x 10 F, a resistor of 5 x 1032, and an inductor of 1 H. The initial charge on the capacitor is zero. If a 3-volt battery is connected to the circuit and the circuit is closed at t = 0, determine the charge on the capacitor at t = 0.001 seconds, at t = 0.01 seconds, and at any time t. Also determine the limiting charge ast → ∞. Enter the exact answer with a < b. The charge at any time is given by the formula Q(t) = (Aeat + Be + C) x 10-6 coulombs, where A = i x 106 coulombs as t→ ∞o x 10 coulombs x 10 coulombs B = i C = i a = i b = i Q(t) → i Round your answers to two decimal places. Q(0.001) = i Q(0.01) = i
Transcribed Image Text:A series circuit has a capacitor of 0.25 x 10 F, a resistor of 5 x 1032, and an inductor of 1 H. The initial charge on the capacitor is zero. If a 3-volt battery is connected to the circuit and the circuit is closed at t = 0, determine the charge on the capacitor at t = 0.001 seconds, at t = 0.01 seconds, and at any time t. Also determine the limiting charge ast → ∞. Enter the exact answer with a < b. The charge at any time is given by the formula Q(t) = (Aeat + Be + C) x 10-6 coulombs, where A = i x 106 coulombs as t→ ∞o x 10 coulombs x 10 coulombs B = i C = i a = i b = i Q(t) → i Round your answers to two decimal places. Q(0.001) = i Q(0.01) = i
If an undamped spring-mass system with a mass that weighs 6 lb lb and a spring constant 9 is suddenly set in motion at t = 0 by an in external force of 99 cos(20t) lb, determine the position of the mass ft at any time t. Assume that g - 32 Solve for u, where u is in feet S² and t is in seconds. u(t) = cos(20 t) - cos(24 t) X
Transcribed Image Text:If an undamped spring-mass system with a mass that weighs 6 lb lb and a spring constant 9 is suddenly set in motion at t = 0 by an in external force of 99 cos(20t) lb, determine the position of the mass ft at any time t. Assume that g - 32 Solve for u, where u is in feet S² and t is in seconds. u(t) = cos(20 t) - cos(24 t) X
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