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Unformatted text preview: tions. 3. Consider the equation of a damped, driven simple harmonic oscillator, m d 2 y dt 2 + dy dt + ky = Fcos ( t ) (4) a) Find the particular solution y ( t ) to this equation. Write your answer in the form y ( t ) = | A | cos ( t + ), and determine expressions for | A | and the phase angle . To keep your work simple, use the denition for the natural frequency of the oscillator = q k m . 1 b) Determine the condition for resonance. In other words, nd an expression for the driving frequency which results in a maximum amplitude | A | for the response. 4. Write down rst-order nite dierence approximations for each of the follow-ing: a) df dx b) d 2 f dx 2 c) d 3 f dx 3 d) t f x 2...
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This note was uploaded on 08/08/2011 for the course PHZ 5156 taught by Professor Johnson,m during the Fall '08 term at University of Central Florida.
- Fall '08