Question

2. Consider the mechanical system illustrated below: x(t) ?y(t) m K 00 The physical values are given as m = 1 kg, k = 100 N/mm, c =10 N/mm/sec. The coordinates of x(t) and y(t) indicate position of the ground and the mass, respectively. Assume frictionless motion of the wheels with the surface beneath and zero initial conditions for y(t=0), x(t=0) and y(t = 0). a) Derive the transfer function between ground X(s) and the mass Y(s). b) Determine the poles and zeros of the system. c) Calculate the damping ratio and natural frequency (hint: You can omit the zero and assume that the numerator is \"1\"). d) Calculate the rise time $t_r$, and maximum overshoot $M_p$ of the system.

          2. Consider the mechanical system illustrated below:
x(t)
?y(t)
m
K
00
The physical values are given as m = 1 kg, k = 100 N/mm, c =10 N/mm/sec. The coordinates of
x(t) and y(t) indicate position of the ground and the mass, respectively. Assume frictionless motion
of the wheels with the surface beneath and zero initial conditions for y(t=0), x(t=0) and y(t = 0).
a) Derive the transfer function between ground X(s) and the mass Y(s).
b) Determine the poles and zeros of the system.
c) Calculate the damping ratio and natural frequency (hint: You can omit the zero and
assume that the numerator is \"1\").
d) Calculate the rise time $t_r$, and maximum overshoot $M_p$ of the system.

2. Consider the mechanical system illustrated below:
x(t)
?y(t)
m
K
00
The physical values are given as m = 1 kg, k = 100 N/mm, c =10 N/mm/sec. The coordinates of
x(t) and y(t) indicate position of the ground and the mass, respectively. Assume frictionless motion
of the wheels with the surface beneath and zero initial conditions for y(t=0), x(t=0) and y(t = 0).
a) Derive the transfer function between ground X(s) and the mass Y(s).
b) Determine the poles and zeros of the system.
c) Calculate the damping ratio and natural frequency (hint: You can omit the zero and
assume that the numerator is 1̈)̈.
d) Calculate the rise time tr, and maximum overshoot Mp of the system.

Added by Patrick S.

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