Unformatted text preview: ω 2 x ( t ) = f ( t ) /m where ω > α > 0, m = 1 and f ( t ) = H ( t + τ )-H ( t-τ ) for τ > 0. Assuming x ( ±∞ ) = ˙ x ( ±∞ ) = 0, use the Fourier transform to ﬁnd x ( t ) for: a) (20 pts) t > τ b) (10 pts) t <-τ c) (20 pts) | t | < τ 5. (25 pts) Consider the temperature in an inﬁnitely long insulated metal rod governed by the heat equation u t = α 2 u xx ,- ∞ < x < ∞ , t > with initial condition u ( x, 0) = 1 x 2 + 1 ,- ∞ < x < ∞ . Use Fourier transform methods to ﬁnd a convolution representation for the time-varying tempera-ture u ( x, t ). Total points: 136...
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This note was uploaded on 11/23/2009 for the course ACM 95b taught by Professor Nilesa.pierce during the Winter '09 term at Caltech.
- Winter '09