370 PRACTICAL MATHEMATICS 



c(b 2 - p 2 ) 



HellCe A - (62,^2 



T Zap A 



Also B = TO ? 



b 2 p 2 



2apc 



(b 2 - p 2 ) 2 + 4a 2 p 2 

 As an example, let a = 2, b = 3, c = 3, and p = 2. 



{MM (lIT 



Then -j-r + 4 -r- + 9x = 3 sin 2t 



dt 2 dt 



Let a; = A sin 2t + B cos 2& 



>y/vt 



Then -=- = 2A cos 2t - 2B sin 2t 



at 



d z x 



and -J-T. = - 4A sin 2Z 4B cos 2f 



" 



cos < 



and 5A - 8B = 3 



8A + 5B = 



A-15 B- -^ 



89' 89 



Thus x = sin 2t cos 2t 



oU o9 



g 



= (5 sin 2t- 8 cos 2t} 

 o9 



3 8 



= 7= sin (2* a), where tan a = - 

 V89 5 



185. A condenser of capacity k is charged so that the potential 

 difference of the plates is V Q . The two plates are connected by 

 a wire. 



If Q is the quantity and C the current, 



Then Q = kv, and C = ^f 



at 



If the connecting wire is of resistance R but of negligible in- 

 ductance, 



, 



Then 



dv 



-**i 



dv v 



