# damped-mass-spring-system

• Dec 10th 2009, 07:22 PM
lord12
damped-mass-spring-system
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.
• Dec 11th 2009, 06:12 AM
HallsofIvy
Quote:

Originally Posted by lord12
1. y" + 14y' + 58y = 0
a) Classify the system as overdamped, underdamped, or critically damped.

The characteristic equation is $r^2+ 14r+ 58= 0$. What are the roots of that? What are the definitions of "overdamped", "underdamped" or "critically damped"?

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.
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:

c) Identify the transeitn solution and the steady state solution. Describe any long term behavior of the system.
What are the definitions of "transient solution" and "steady state solution"?