A rotational mechanical system is described by the 2nd order differential equation, d²0(t) d0(t) +B + KO(t) = T,(t) dt dt2 where T(t) is the input torque, e(t) is the output angular displacement and J, B and K are the system inertia, damping constant and spring constant respectively. The system is initially at rest, i.e. 0(t) = O and de(e) = 0. At time t = 0, the input torque to the system undergoes a step change from 0 to dt 12 Nm. The resultant angular displacement of the system due to the applied torque is shown on Figure Q2. (1) Find the spring constant 'K', the damping ratio 'c', system Inertia 'J' and damping constant 'B'. Displacement response of rotational mechanical system 0.12 0.1 .0.08 0.06 80.04 0.02H 0.5 1.5 2 2.5 3.5 4.5 5 Tme (seconds) Figure Q2 Displacement (rad)

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A rotational mechanical system is described by the 2nd order differential equation,
d²e(t)
dt2
+ B.
dt
de(t)
+ KO(t) = T,(t)
where T(t) is the input torque, 0(t) is the output angular displacement and J, B and K are the system
inertia, damping constant and spring constant respectively. The system is initially at rest, i.e. 0(t) =
O and
de(t)
= 0. At time t = 0, the input torque to the system undergoes a step change from 0 to
dt
12 Nm. The resultant angular displacement of the system due to the applied torque is shown on
Figure Q2.
(1) Find the spring constant 'K', the damping ratio 'c', system Inertia 'J' and damping constant 'B'.
Displacement response of rotational mechanical system
0.12
0.1
.0.08
0.06
0.04
0.02-
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Time (seconds)
Figure Q2
Displacement (rad)
Transcribed Image Text:A rotational mechanical system is described by the 2nd order differential equation, d²e(t) dt2 + B. dt de(t) + KO(t) = T,(t) where T(t) is the input torque, 0(t) is the output angular displacement and J, B and K are the system inertia, damping constant and spring constant respectively. The system is initially at rest, i.e. 0(t) = O and de(t) = 0. At time t = 0, the input torque to the system undergoes a step change from 0 to dt 12 Nm. The resultant angular displacement of the system due to the applied torque is shown on Figure Q2. (1) Find the spring constant 'K', the damping ratio 'c', system Inertia 'J' and damping constant 'B'. Displacement response of rotational mechanical system 0.12 0.1 .0.08 0.06 0.04 0.02- 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Time (seconds) Figure Q2 Displacement (rad)
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