354 PRACTICAL MATHEMATICS 



= a cos nt, and this satisfies the condition x = a cos nt, and con- 

 sequently -p- = n z x. 



Here again the motion of the body is the horizontal projection 

 of the motion of a particle describing a circular path of radius a 

 with uniform angular velocity n radians per second. 



The periodic time = 

 n 



Frequency 



n 



Amplitude = a 



(3) Let the initial conditions be x = a and v = v when t = 0. 

 Then x = A sin nt + B cos nt 



and x = a when t = 0, then B = a 



dec 



Also v = -r = wA cos nt nB sin nt 



at 



and t> = v n when < = 0, then A = 



n 





The final solution is x = sin 

 n 



+ a cos 



na 



where tan e = 

 v n 



FIG. 117. 



If a circle be drawn of radius -y a 2 + () and OQ is a radius 

 inclined at an angle e to the vertical diameter, while OP is another 



