Suppose we have a temperature model where t is measured in h

Suppose we have a temperature model where t is measured in hours: f(t) = A sin (B t - C) + D The period is P = 24 hrs. What is the value of B? The average temperature over P is 50 degrees. What is D? Suppose the phase shift is zero. Suppose the minimum temperature is 25 degrees and it occurs at t = 6. What is the value of C and A? What is the maximum temperature? Now suppose the min. and max. are the same, but the minimum temperature (25 degree) occurs at t = 5. Now what is the value of C?

Solution

a) T = 24 hours

Therefore B = 2.pi/T = 2.pi/24 = pi/12

b) Since the average is 50 degrees, hence D = 50

c) Phase shift = 0 => C/(pi/12) = 0 => C = 0

Therefore eqn reduces to f(t) = Asin[(pi/12).t] + 50

25 = Asin[(pi/12)*6] + 50

-25 = Asin.pi/2

=> A = 25

maximum temperature = A + 50 = 75