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I did a problem where I was asked to model a simple cooling graph. No big deal. I got my model and found my constant values by using initial values.
Now comes the sticky part. I am asked to create a model similar to the previous simple cooling problem for a more complex system. Keep in mind this is a first course in DE and its only the second week.
The problem is now that the ambient temperature is fluctuating. I have established a sinusoidal function to model the ambient temperature and have begun setting up my model. I am given no initial conditions of the object, I am told that no matter what the initial values are, the function becomes closer and closer to a specific harmonic function with the same period as the ambient temperatures harmonic function.
I am asked explicitly to give a model for the temp of the object with respect to time. Now, pardon me for not using LaTeX, I am pretty new here... but this is my model as of now.
dT/dt = k*(T - 80 + 30*cos(2*pi*t/24))
Ill be honest, I suck at algebra. But am I supposed to carry this further and develop anything else? I am given no k value, no initial temps, no max/min temps, no intersection points (dT/dt = 0) and basically nothing else. I am assuming my book is just wanting me to set up the basics of the DE and the 'modeling' part was in getting the [80 + 30*cos(2*pi*t/24)] part. What do you think?
Now comes the sticky part. I am asked to create a model similar to the previous simple cooling problem for a more complex system. Keep in mind this is a first course in DE and its only the second week.
The problem is now that the ambient temperature is fluctuating. I have established a sinusoidal function to model the ambient temperature and have begun setting up my model. I am given no initial conditions of the object, I am told that no matter what the initial values are, the function becomes closer and closer to a specific harmonic function with the same period as the ambient temperatures harmonic function.
I am asked explicitly to give a model for the temp of the object with respect to time. Now, pardon me for not using LaTeX, I am pretty new here... but this is my model as of now.
dT/dt = k*(T - 80 + 30*cos(2*pi*t/24))
Ill be honest, I suck at algebra. But am I supposed to carry this further and develop anything else? I am given no k value, no initial temps, no max/min temps, no intersection points (dT/dt = 0) and basically nothing else. I am assuming my book is just wanting me to set up the basics of the DE and the 'modeling' part was in getting the [80 + 30*cos(2*pi*t/24)] part. What do you think?