Forced and Unforced systems Flashcards

1
Q

Unforced systems ODE

A

linear homogeneous ODEs with constant coefficients that can be solved using the exponential trial solution method: y= Ce^(lamba*t)

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2
Q

Repeated root in general solution

A

need to multiply one part of solution by t due to repeated real roots

e.g y= C1e^3t + C2e^3t
y’ =3C1e^3t +C2e^3t + 3C2e^3t

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3
Q

Order

A

highest power or derivative in equation

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4
Q

Linearity

A

whether dependent variable has unusual non linear functions, such as y^2, or siny or 1/y

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5
Q

Homogeneity

A

Take all of the terms in the equation containing dependent variable to LHS, if RHS = 0 , then equation is homogeneous, If there are terms involving t (or constants) remaining on the RHS the equation is nonhomogeneous

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6
Q

Car suspension system

A

Overdamping: After being released from the initial disturbance, the suspension system is slow to return to the undisturbed state. No oscillation.

Critical damping: After being released from the initial disturbance, has large displacement initially, but isquick to return to the undisturbed state. No oscillation.

Underdamping: Oscillates around an equilibrium point slowly returning to the undisturbed state.

No Damping: The car will keep oscillating around the equilibrium point, at the same magnitude forever.

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7
Q

Car suspension system table

A

Overdamping c>4mk two real roots
Critical damping c= 4mk two equal roots
Underdamping c<4mk two complex roots
No damping c = 0 two purely imaginary roots

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