Example 1.0 for the linear translational mechanical system given below figure 1 with the parameter values m =1 kg, c= 1 N-s/m, and k = 10 N/m. Find The un damped natural frequency and dimensionless damping ratio?? At) Figure 1 Mechanical System 1 x1(t) + x2(t) k u(t) k x2(t). m m m y0) = [1 0]] x1(t) x2(t) 1 The associated transfer function is given by k H(s) = s2 + +

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Example 1.0 for the linear translational mechanical system given below figure 1 with the
parameter values m = 1 kg, c = 1 N-s/m, and k = 10 N/m. Find The un damped natural frequency
and dimensionless damping ratio??
Figure 1 Mechanical System
1
*1(t)
x2(t)
(1)'s
+
x2(t)
k
u(t)
m
m
y0) = |1 0]
x1 (t)
x2(t)
1
The associated transfer function is given by
H(s)
s2 +
Find
a) Zeta š
b) natural frequency w,
c) damped natural frequency wa
d) roots (poles)
e) settling time T,± 2% ±5%
f) %overshoot Po
g) peak time T,
All work carried out must be shown, just answers will not
be accepted or marked
Transcribed Image Text:Example 1.0 for the linear translational mechanical system given below figure 1 with the parameter values m = 1 kg, c = 1 N-s/m, and k = 10 N/m. Find The un damped natural frequency and dimensionless damping ratio?? Figure 1 Mechanical System 1 *1(t) x2(t) (1)'s + x2(t) k u(t) m m y0) = |1 0] x1 (t) x2(t) 1 The associated transfer function is given by H(s) s2 + Find a) Zeta š b) natural frequency w, c) damped natural frequency wa d) roots (poles) e) settling time T,± 2% ±5% f) %overshoot Po g) peak time T, All work carried out must be shown, just answers will not be accepted or marked
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