Unformatted text preview: cellar. We assume that the ambient temperature varies sinusoidally about a certain mean, and we wish to compute the interior temperature. Problem 0121 – 2 . Assume we have a sealed root cellar and that the ambient temperature varies sinusoidally about a mean A with the amplitude of the ﬂuctuation given by A 1 . Then A ( t ) = A + A 1 sin( ωt ) Compute the resulting temperature T in the root cellar (in terms of A , A 1 , k and a parameter determined by initial conditions). Identify the steady state component of T ( t ) and compute the phase shift and the attenuation factor in the case A = 18 ◦ C, A 1 = 4 ◦ C, ω = 5 π , k = 3. You may assume T (0) = 0 if you wish – it makes no diFerence. The graph below show the ambient A ( t ) and the response T ( t ). You can use it as a rough check on your calculations. 5 10 15 20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 t...
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 Winter '09
 Rate Of Change

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