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

  1. Nov 15, 2009 #1
    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 :blushing:


    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.
     
  2. jcsd
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