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Math Help - damped-mass-spring-system

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by lord12 View Post
    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"?

    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).

    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"?
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