Answered: Differential Equations | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 18EQ

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Question

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

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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