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lecture_22 (dragged) 1 - We discuss a steady-state solution...

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2 MA 36600 LECTURE NOTES: MONDAY, MARCH 9 Figure 2. Graph of Steady-State Solution U ( t ) = 9 cos t -2.5 0 2.5 5 7.5 10 12.5 1 -10 -5 5 10 Figure 3. Graph of Solution u ( t )= u c ( t )+ U ( t ) -2.5 0 2.5 5 7.5 10 12.5 1 -10 -5 5 10 We have considered the equation u °° + ω 2 0 u = F 0 m cos ωt when ω ° = ω 0 , but what if ω = ω 0 i.e., we apply an external force oscillating at the natural frequency?
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Unformatted text preview: We discuss a steady-state solution U ( t ). Again, we may use the Methods of Variation of Parameters or Undetermined Coecients, but we opt for a diFerent trick....
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