362 Mr ROHRS, on THE MOTION OF BEAMS 



Now -~: , (or dropping the accent and assuming y for the dynamical deflection) 



d'y :, d*y ^ , 



-—- and — — are both = when s = and s = a, 



ds* ds* 



because the beam is at rest at those points, and the radius of curvature is infinite there, 



fd*y , ^ d^y , . d*y 



I -~ = 0, * = 0, and s = a, •.• y and .•. — - = at those points ; -— = 0, •.• r is = 



\CE^ ttio CIS 



there except for one instant). 



Therefore expanding y in a series of the form 



2 IP, sin — j , 



we have 



m — — ■= - 6' — — P„+ — sin . 



dt' a* a a 



_ _ ^ . ■TT^n'bt „ , Trnvt 



Let F, = A„ sin + B^ sin , 



, I Vma" « 



where ^„ and S, are constants to be determined. , 



If now the breadth of the girder be assumed = 1, and W be its weight, 5' the central 

 deflection for the weight W, 



y _Wa' 5 



¥ 384 ' 



mag- = W; 



. ° 5,384 



SQ 



a 



5„ 



a 384,^' a^g 



Again, because the girder has no initial velocity, 



■7rV6 ^ irnv „ 

 Vma <* 



•n-na ^ 5^ 

 2 X 48^ 



irV - -— wW — —- 

 if S be the deflection due to a weight Q at centre of the girder. 



