EXAMPLES XXII 



401 



0_ 



periodic time T = . What is the average value of y 3 during 



the periodic time ? 



(4) If y = a cos qt and x = b cos (qt c) where / is time and 

 a, q, b, c are constants. Find the average value of xy during 



Q_ 



the periodic time T = . What is the average value of x 2 during 



the periodic time ? 



(5) If y=acosqt and x=bsin(qt c) where / is time and 

 a, q, b, c are constants. Find the average value of xy during the 



periodic time T = . What is the average value of x* during 



the periodic time ? 



(6) Find p. sine series for y = mx 2 between x = and x = TC. 



(7) Find a sine series for y = mx 3 between x = and x = TC. 



(8) Find a cosine series for y = mx 3 between x = and 



X= TC. 



(9) Find a cosine series for y = e* between x = and x = TC. 



(10) Find a cosine series for y = e"* between x = and x = TC. 



(11) Find a Fourier's series for y = x 2 between x = TC and 



X = TC. 



(12) Find a Fourier's series for y = x 3 between x = TC and 



x = TC. 



(13) Find a Fourier's series for y = e~ x between x TC and 



X = TC. 



(14) Find a sine series for y = x between x = and x = c. 



(15) Find a cosine series for y = x z between x = and x = c. 

 The value of a periodic function of t is given below for twelve 



equidistant values of t covering the whole period. 



Neglecting terms of the fourth and higher orders, express it 

 in a Fourier's series for the six different examples. 



(16) 



(17) 



(18) 



2 C 



