How to solve this mathematical problem using the trigonometric method?

Asked Dec 02 '20 at 19:33

Active Dec 02 '20 at 22:31

Viewed 101 times

I am a high school student that is doing Newton’s law of cooling for his school report. I passed by a website that is finding the general formula [T(t)] with an approximation of the environmental temperature. Everything was mostly understandable but at one point, the person used Mathcad to solve the integrals. I am therefore interested on how this mathematical process can be carried out analytically so please if you have any idea of how to solve it analytically let me know.

Website: http://calculus7.com/sitebuildercontent/sitebuilderfiles/nwtnslawcling1.pdf

Equation I have(assuming k = 0.128):

The way I would like it to be:

note: the graph I trying to get is for cooling and the website is using heating instead of cooling. Note 2: on my equation, T(t) is supposed to be the same thing as y(t) in the equation from the website.

edited Dec 02 '20 at 22:31

asked Dec 02 '20 at 19:33

General MO7

I think both integrals should have closed (analytic) form – Vasili Dec 02 '20 at 19:46
Is your problem very similar to Example 2? – PTDS Dec 02 '20 at 20:02
Yes that’s it.. – General MO7 Dec 02 '20 at 20:05
1

In that case, please post $T(t)$, initial temperature $y(0)$ and $k$ – PTDS Dec 02 '20 at 20:07
I don’t quiet understand what you mean? – General MO7 Dec 02 '20 at 20:22
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It looks like the expressions you posted are not quite correct. If you post the three inputs mentioned earlier, it will be easier to solve the problem. – PTDS Dec 02 '20 at 20:23
Oh I realized thanks a lot for letting me know. – General MO7 Dec 02 '20 at 20:26
No answer?????? – General MO7 Dec 02 '20 at 21:03
Are you sure about the factor $e^{0.269}$? Should it be $e^{0.269t}$ instead? – PTDS Dec 02 '20 at 21:06
Sorry again I had a writing error I will change it. – General MO7 Dec 02 '20 at 21:09
Do you know how to solve it by the way? – General MO7 Dec 02 '20 at 21:09
1

Probably I do... – PTDS Dec 02 '20 at 21:10
Let us continue this discussion in chat. – PTDS Dec 02 '20 at 21:12
See https://math.stackexchange.com/questions/4961/interesting-results-easily-achieved-using-complex-numbers. – Integreek Nov 16 '24 at 06:01

How to solve this mathematical problem using the trigonometric method?

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