Second Order System

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

y(t) Output Behaviour of Second Order Sin response to step change { 0 < ζ < 1 }

Output

Time, s

y(t)

Second Order System2nd Order System Behaviour with step input

Equation :For 0 < z < 0y(t) = A (1 - exp (-z x / r) * (cos (sqrt(z2 - 1) /r * x ) + z / sqrt (1 - z) sin (sqrt(z2 - 1) / r * x) ) )

Result :Chart 1 : Output Response ( 0 < z < 1 )

Calculations :t A r z 1 - z2 sqrt( 1 - z2 ) 1-z sqrt( 1 - z ) Output

1 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.3155845172 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.8337621463 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 1.1252782674 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 1.0826729415 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.8661524416 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.6902025157 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.6575481738 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.7338342169 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.824736646

10 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.86318547411 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.84388365212 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.80257447213 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.7757825614 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.77586849215 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.79219869416 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.8073658917 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.81159654518 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.80634003419 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.79887508420 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.79510618321 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.79612138822 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.79935348723 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.80174996424 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.8020230525 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.80082402226 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.79954092527 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.7990723628 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.79941390729 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.80001641930 0.8 0.8 0.2 0.5527864 0.74349607 0.8 0.89442719 0.800370786