Question i have states - State the periods and frequencies and suggest an application that the functions might occur in
a) 0.001cos(512 Pi t)
b)3+5sin((24/2Pi)t) where t is measured in hours
2007-02-12 22:33:14 · 3 answers · asked by Perfect-Angel84 2 in Science & Mathematics ➔ Mathematics
a) amplitude is .001. Frequency is 512 pi. Period is (1/512 pi)(2pi) = .0039 time units.
b) amplitude is 5. Vertical offset is 3. Frequency is 24/2pi. Period is (2pi/24)(2pi) = pi^2 / 6 hours
these are examples of modeling predictable cyclical patterns: ie, Hours of daylight at a specific latitude throughout the year; the position at a point on a mechanical mechanism relative to a fixed point, etc
2007-02-13 03:36:28 · answer #1 · answered by davidosterberg1 6 · 0⤊ 0⤋
512pi = 2pi*f so f= 256 Hz
T(period) = 1/f =3.906*10^-3 s
You must bring the expression units of time in seconds
As 1 hour = 3600 s
b) 24/2*3600 pi=2pi*f f= 6*3600Hz=2.16*10^4 Hz
T = 4.63*10^-5 s
2007-02-13 10:52:30 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋
(f is the frrequency and T is the period, which is 1/f)
512*pi = 2*pi*f
f = 107.5 Hz
T = 1/f --> T = 9.3 msec (milli seconds=10^-3)
24/(2pi) = 2*pi*f
f = 0.6 Hz
T = 1.67 seconds
2007-02-13 06:52:48 · answer #3 · answered by cp_exit_105 4 · 1⤊ 0⤋