An ODE for Newton’s law of cooling, ??/?? + ?? = ??(?) relates indoor temperature changes...

An ODE for Newton’s law of cooling, ??/?? + ?? = ??(?) relates indoor temperature changes u(t) to outdoor temperature changes modeled by the function ?(?) = ? + ? cos(??) + ? sin(??). k is a constant that measures how well a building is insulated and t is time in hours. Suppose your air-conditioner is broken. You want to find out how outdoor temperature effects the temperature in your house by doing the following:

(a) Find a model for outdoor temperature, A(t). Specifically find a, b and c. Use ω = π/12 for a 24-hour time period. Use estimates of the high and low temperature of your current location. Assume the high temperature occurs at 4 pm.

(b) Solve the ODE above for u(t). Use k = 0.3 (a typically insulated building) and your equation from part (a). Use u(0) = temperature at midnight in your location for the initial condition.

(c) Create a graph with both your solution function and the outdoor temperature function.

(d) When does the maximum indoor temperature occur?

Expert Solution

Amanda K answered 6 months ago

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