SOLUTION: Determine the average and rms values for the function: y(t)=25+10 sin 6pi*t

Algebra ->  Equations -> SOLUTION: Determine the average and rms values for the function: y(t)=25+10 sin 6pi*t      Log On


   

Question 1070645: Determine the average and rms values for the function:

y(t)=25+10 sin 6pi*t
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Integrate the function over one period and divide by the length,
int%28%2825%2B10sin%286pi%2At%29%29%2Cdt%29=25t-%285%2F%283pi%29%29cos%286pi%2At%29%29%2BC
Integrating from t=0 to t=%282pi%29%2F%286pi%29=1%2F3,
A=25%281%2F3-0%29-%285%2F%283pi%29%29%28cos%282pi%29-cos%280%29%29=25%2F3
f%5Bave%5D=A%2F%281%2F3-0%29=%2825%2F3%29%2F%281%2F3%29=25%2F3
.
.
.
Integrate the square of the function over one period and divide by the length,
then take the square root,

Integrating from t=0 to t=1%2F3,

f%5BRMS%5D=sqrt%28225%2F%281%2F3%29%29=sqrt%28675%29=15sqrt%283%29