678 BELL SYSTEM TECHNICAL JOURNAL 



then 



xi{t) — sF{s) (initial value being zero) 



The Laplace transform of equation (27) is 



The solution of (28) is made easier if it is written in the form 



{s + ay + jS^ 

 in which • 



a= I and a^ -\- ^^ = o)\ 



Subjecting this system to a triangular whip, of which the Laplace trans- 

 form is 



we have 



the solution of which involves two transform pairs. The inverse transform 

 gives us a solution of the transient as well as the steady state. It has been 

 mentioned before that the steady state produces the maximum displace- 

 ments across the mount; therefore it will be considered in more detail. We 

 find that the steady state solution is 



Xait) =-^---( -sin ^t + 2e"^ sin ^(/ - b) - e'"' sin ^(/ - 26) j (31) 



Which simplifies to 



-at 



Xait) = V ^ VWn^) sin {(3t - e) (32) 



Using dimensionless quantities 



