588 Prof. T. R. Lyle on Mechanical Analogy to the 



the pendulum; and when the electromagnets are energized by 

 such a current the mutual stress between the beam and the 

 pendulum will be approximately a pure couple. 



14. If the mutual stress between the beam and the pendulum 

 be the periodic couple P = p cosa^ the equations of motion of 

 the system can easily be shown to be 



(M -f m x + m 2 ) x—mji^ + m 2 l 2 0=:O 



-*,+ —7—^1 + ^1 = \ 



v + l 2 2 +g6 2 = O, 



where m 1 is the mass of the first pendulum as before, k its 

 radius of gyration round its centre of mass, and h the distance 

 of its centre of mass below the knife-edo-es. 

 p _|_ j L 2 

 Putting l x for — r- — . the length of the simple pendulum 



equivalent to the compound one, and proceeding exactly as 

 in § 5, we obtain the following equations connecting X , 2r 

 and P, 



whe 



re 



2 _ M + m Y -f- m 2 m 2 l-2 



^ '" iN. + m 1 + mdli — m 1 Ji9 m ' Pl = ~(M. + m l + m a )l 1 -m 1 ti 



2 _ M 4- nix + m 2 g n%i h 



1 M. + m 1 + m 2 



^ mji (M.-{-mi + in 2 ) — m l li 



[Note. 61 must always be kept less than the angle of 

 friction between the knife-edge and the plane on which it 

 bears.] 



15. If a periodic E.M.F. = P = ^ cos at act on the receiving- 

 circuit of a wireless receiver, the equations for the currents 

 in the circuits are (see §§ 1, 2) 



nC^-MDC + P, 

 r 2 C 2 =-MDC l5 



