# Metal Heat Treatment: How to create a sinusoidal function that increases in frequency

1. Nov 15, 2009

### babygotjack5

Alright, this is a hypothetical problem for my math class, (but it seemed to fit here better than calculus help) and though I am allowed to site sources, I don't necessarily want the answer just given to me (I mean, I'd really like to figure it out).

1. The problem statement, all variables and given/known data
• Treatment lasts 15 hours.
• Oven starts at 300 degrees
• Oven ends at 100 degrees
• Max temperature: 500
• Min temperature: 50
• Temperature change cannot be more than 4 degrees C per minute over the course of 10 min
• It must increase gradually for the first few hours, then fluctuate rapidly as it approaches 100 degrees.

2. Relevant equations
This is what I'm looking for

3. The attempt at a solution
My attempts thus far consist of drawings of what the function should look like. From what I can tell, this is a cos (or sin) function that decreases in altitude as it increases in frequency (the function of a wave?) and has a slight downward slope.

So, my question is, how does one "make" such a function? I am inclined to think that it must be like an "linear-exponential-sinusoidal" function, but I'm not sure how to plug it in all together.