Summary: Math 308 plots
February 3, 2009.
The three plots on this page are of the external temperature
M(t) = 48 - 13 cos(t),
internal temperature
T(t) = 54 - 10.2 cos(t - 0.5) + 11.5e-t/2
,
and the oscillatory (long-term) component of the internal temperature
Tosc(t) = 54 - 10.2 cos(t - 0.5).
The governing ODE is
dT
dt
= K(M(t) - T(t)) + H0,
where
M(t) = M0 - B cos(t)
and the time constant 1/K = 2 hours.
0 5 10 15 20 25 30 35 40 45 50
35
40
45