Suppose that your air conditioner fails on Sunday at midnight (t0 = 0), and you cannot afford...
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Suppose that your air conditioner fails on Sunday at midnight(t0 = 0),
and you cannot afford to have it repaired until payday at the endof
the month. Assume that the outside temperature varies accordingto
the function
A(t) = 80 5 cos(?/12)-5?3sin(?/12t)
and that your inside temperature, u(t) obeys Newton’s law ofcooling
and is governed by the differential equation
du/dt= -0.2(u-A(t))
(a) If your indoor temperature when the air conditioner failedwas
70?F , determine the dynamics of temperature inside yourapart-
ment over time. i.e. find a particular solution to the initialvalue
problem.
(b) What will the temperature inside the apartment be, 24 hoursafter
the break down?
(c) In the long run (t ? ?), what is the maximum and minimum
temperature you can anticipate inside your apartment?
Suppose that your air conditioner fails on Sunday at midnight(t0 = 0),
and you cannot afford to have it repaired until payday at the endof
the month. Assume that the outside temperature varies accordingto
the function
A(t) = 80 5 cos(?/12)-5?3sin(?/12t)
and that your inside temperature, u(t) obeys Newton’s law ofcooling
and is governed by the differential equation
du/dt= -0.2(u-A(t))
(a) If your indoor temperature when the air conditioner failedwas
70?F , determine the dynamics of temperature inside yourapart-
ment over time. i.e. find a particular solution to the initialvalue
problem.
(b) What will the temperature inside the apartment be, 24 hoursafter
the break down?
(c) In the long run (t ? ?), what is the maximum and minimum
temperature you can anticipate inside your apartment?
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