Calculus 1 - Lesson 9/10/11 - second order linear DE's

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9 Homogeneous, 10 nonhomogeneous, 11 applications

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10 Terms

1
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<p>What is characteristic equation of this DE?</p>

What is characteristic equation of this DE?

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2
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<p>What is the general solution to this?</p>

What is the general solution to this?

2 different e powers with constants

<p>2 different e powers with constants</p>
3
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<p>What is the general solution to this?</p>

What is the general solution to this?

2 equal e powers, one with added x

<p>2 equal e powers, one with added x</p>
4
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<p>What is the general solution to this?</p>

What is the general solution to this?

E power with sin/cos

<p>E power with sin/cos</p>
5
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<p>Recap</p>

Recap

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6
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<p>How do we solve this nonhomogeneous equation?</p>

How do we solve this nonhomogeneous equation?

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7
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What if one of the terms in the guess of yp is in the solution of yc?

Add a t to the repeated term

8
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<p>Give the DE acccording to Newton</p>

Give the DE acccording to Newton

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9
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When is system:

  • overdamped

  • critical damped

  • underdamped

  • overdamped: D van char.eq. > 0

  • critical damped: D chareq = 0

  • underdamped: D chareq < 0

10
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When does resonance occur?

c = 0

f;res = periodic force (sin(ax))

if beta is same as a: t needs to be added in y_p. with large t, y will be very large