--> //initializations

--> k=25000 //KN/m (stiffness)
 k  = 

   25000.


--> D=0.5 //(damping factor)
 D  = 

   0.5


--> m=30 //KN (mass of foundation block)
 m  = 

   30.


--> printf('NOTE: given 3.0sin(30t) and actual expression is Fosin(wt)')
NOTE: given 3.0sin(30t) and actual expression is Fosin(wt)
--> Fo=3.0 //KN (force)
 Fo  = 

   3.


--> w=30 //radian/sec 
 w  = 

   30.


--> g=9.81
 g  = 

   9.81


--> //calculations

--> wn=sqrt((k*10^3*g)/(m*10^3)) //(circular frequency)
 wn  = 

   90.415707


--> fn=wn/(2*%pi) //(natural frequency)
 fn  = 

   14.390107


--> T=1/fn //(natural period)
 T  = 

   0.0694922


--> r=w/wn // (ratio of frequency)
 r  = 

   0.3318008


--> M=1/sqrt((1-r^2)^2+(4*D^2*r^2)) //(magnification factor)
 M  = 

   1.0529067


--> ds=(Fo*100)/k //(static deflection)
 ds  = 

   0.012


--> Am=M*ds //(amplitude of vertical displacement)
 Am  = 

   0.0126349


--> //results

--> printf('natural frequency=%f',fn) //circles/sec
natural frequency=14.390107
--> printf('natural period=%f',T) //sec
natural period=0.069492
--> printf('natural circular frequency=%f',wn) //rad/sec
natural circular frequency=90.415707
--> printf('amplitude of vertical displacement=%f',Am) //cm
amplitude of vertical displacement=0.012635
