The original complementary solution is:

z'' + (B/M)z' + (K/M)z = 0

for this equation the damping ratio is

E = B/2sqrt(MK)

the undamped natural frequency is

w = srqt(K/M)

Both E and w depend on the mass M and the spring constant K. The dashpot coefficient only effect the damping ratio and not the frequency . So the larger is B the higher is damping ratio.

The following graphs illustrate the effect of the values of K and B on the ride.

Note: x-axis: time t, sec, y-axis: output x(t)

K=CONST


B=80 ----- B=1500

B=2500 ----- B=3800

B=CONST

K=1000 ----- K=2000

K=3000 ----- K=4000

Topics:

• Case study Analysis
• Definition of system equations
• Definition of system state variables, output and input-output equations
• System solution
• Laplace Transforms
• System behavior and stability