454 BELL SYSTEM TECHNICAL JOURNAL 



The strain at the attached end of the bar is 



= [-1 



f . nirat 

 v] Wit . , 4 -^-^ ^^ \ ,. ^ .^s 



/ _ _ IT mra \ 

 \ 0)2 ' 2co2^ / 



It may be verified that the sum of the series in (4.3.11) is given by 

 tiTat 



A " ^^^ 2f at 



52 —5 = tan — sin C02/ + cos u^t — 1, (4.3.12) 



It should be observed that the summation is vaUd only in the interval < 

 / < 21/ a. However, the series is periodic with half period 21/ a and includes 

 only the odd terms, so that the function repeats itself with reversed sign 

 after each interval 21/ a. Hence the summation, valid for all t, can be 

 written 



rnrat 

 4 ^ '^^17 



TT n=l,3,B- 



m) - ■] 



("1) tan — sm C02 U - — ) + cos C02 U — — j- 1 



t -"—]- \\ (4.3.13) 



, 2mt ^ ^ ^ 2{m + \)l 



k = m when < t < 



a a 



w = 0, 1, 2, 3, • • • . 



We may, therefore, rewrite (4.3.11) in the form 



ea (Jilt 



— = —tan 



— sm aj2^ + ( — 1 ) tan — sm «2 1 / — — 1 

 a L ^ \ CL / 



('-t)-0 



+ cosco2(/ - — - 1 (4.3.14) 



