Consider the differential equation 5x + 2x +x=2+3t, with initial conditions x(0) = 0, i(0) = 2. Give: (a) Its particular solution xp (t). Does xp (t) depend on the initial conditions?
Consider the differential equation 5x + 2x +x=2+3t, with initial conditions x(0) = 0, i(0) = 2. Give: (a) Its particular solution xp (t). Does xp (t) depend on the initial conditions?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 1CR
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Transcribed Image Text:Consider the differential equation
5x + 2x +x = 2 + 3t,
with initial conditions x(0) = 0, i(0) = 2. Give:
(a) Its particular solution xp(t). Does xp (t) depend on the initial conditions?
(b) Its homogeneous solution xh(t)
(c) The time constant, natural frequency, damping ratio, and damped natural frequency if applicable.
Give units.
(d) The complete solution, giving values for the integration constants. Hint: it may reduce the amount
of work required if you start by writing the homogeneous solution in the form that involves the
damped natural frequency.
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