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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 + γ dy dt + ky = Fcos ( ωt ) (4) a) Find the particular solution y ( t ) to this equation. Write your answer in the form y ( t ) = | A | cos ( ωt + δ ), and determine expressions for | A | and the phase angle δ . To keep your work simple, use the deﬁnition for the natural frequency of the oscillator ω = q k m . 1 b) Determine the condition for resonance. In other words, ﬁnd an expression for the driving frequency ω which results in a maximum amplitude | A | for the response. 4. Write down ﬁrst-order ﬁnite diﬀerence 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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- Fall '08
- Differential Equations, ORDINARY DIFFERENTIAL EQUATIONS, Simple Harmonic Oscillator, first-order differential equations