I am having trouble getting started with this: The average daily HIGH temperatur

Question

I am having trouble getting started with this: The average daily HIGH temperature in Philadelphia oscillatesbetween a low of 32 degrees (in January, m=0) to a high of 81degrees (in July, m=6) a) Assume that the average daily hihg temperature, H(m)(indegrees F) is a periodic function of the month, m. Create afunction that models this scenario. I have calculated the midline at 56.5 degrees and theamplitude at 24.5 degrees. I came up with the following which I do not hink is right: m =24.5 cos (t) +56.5 I am having trouble getting started with this: The average daily HIGH temperature in Philadelphia oscillatesbetween a low of 32 degrees (in January, m=0) to a high of 81degrees (in July, m=6) a) Assume that the average daily hihg temperature, H(m)(indegrees F) is a periodic function of the month, m. Create afunction that models this scenario. I have calculated the midline at 56.5 degrees and theamplitude at 24.5 degrees. I came up with the following which I do not hink is right: m =24.5 cos (t) +56.5

Explanation / Answer

You were very close. The 24.5cos(f(m))+56.5 is correct. But the something needs to be such that cos(f(m)) = -1 when m = 0 =12 = .. gives -1, and cos(f(m)) = 1 when cos = 6,18,... So f(m) = (pi/6)m+pi, and the final answer is T =24.5cos((pi/6)m+pi) +56.5 In general, you can write harmonic oscillation as Acos(wt + phi) +B, where w,phi,A,B are constants that are adjusted to fit theinitial conditions.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.