Figure Q1 shows a forced spring-mass system with damping, where mass m = 1 kg, spring constant k = 0.2 N/m, and damping coefficient c = 0.3 N.s/m. (a) This forced spring-mass system with damping can be described by the following differential equation: Determine: (i) (ii) d²x(t) c_dx(t) k dt² m dt - + ~x(t) = - m - F(t) m Laplace Transfer Function of this system, This system's steady state gain, damping ratio and natural frequency. (b) Sketch frequency response of the system from part (a) in the form of Bode plot as accurately as you can.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Q1
X
Determine:
k
(i)
(ii)
m
CA
Figure Q1
Figure Q1 shows a forced spring-mass system with damping, where
mass m = 1 kg, spring constant k = 0.2 N/m, and damping coefficient c
= 0.3 N-s/m.
F
(a) This forced spring-mass system with damping can be described
by the following differential equation:
d²x(t) c dx(t), k
- + − x(t):
dt² m dt m
+
1
- F(t)
==
m
Laplace Transfer Function of this system,
This system's steady state gain, damping ratio and natural
frequency.
(b) Sketch frequency response of the system from part (a) in the form
of Bode plot as accurately as you can.
Transcribed Image Text:Q1 X Determine: k (i) (ii) m CA Figure Q1 Figure Q1 shows a forced spring-mass system with damping, where mass m = 1 kg, spring constant k = 0.2 N/m, and damping coefficient c = 0.3 N-s/m. F (a) This forced spring-mass system with damping can be described by the following differential equation: d²x(t) c dx(t), k - + − x(t): dt² m dt m + 1 - F(t) == m Laplace Transfer Function of this system, This system's steady state gain, damping ratio and natural frequency. (b) Sketch frequency response of the system from part (a) in the form of Bode plot as accurately as you can.
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