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1. y" + 14y' + 58y = 0
a) Classify the system as overdamped, underdamped, or critically damped.
b) Suppose an external service F(t) = 71cos(t) + 43sin(t) is applied to the system above. Find the general solution to the resulting non-homogeneous differential equation.
c) Identify the transeitn solution and the steady state solution. Describe any long term behavior of the system.
The characteristic equation isQuote:
Originally Posted by lord12
. What are the roots of that? What are the definitions of "overdamped", "underdamped" or "critically damped"?
Since "i" is NOT a root of the characteristic equation above, just look for a particular solution of the form Acos(t)+ B sin(t).Quote:
b) Suppose an external service F(t) = 71cos(t) + 43sin(t) is applied to the system above. Find the general solution to the resulting non-homogeneous differential equation.
What are the definitions of "transient solution" and "steady state solution"?Quote:
c) Identify the transeitn solution and the steady state solution. Describe any long term behavior of the system.