Given the torsional system shown below actuated by a step input torc T(t): T(O) O0) fro> K D 1- Write first the equation of motion, and then: 2- for K=2 N.m/rad, find J and D to yield 15% overshoot and a 2% settling time of 5 seconds, and then calculate the resultant natural frequency and damping ratio. 3- for K=2 N.m/rad, find J and D to yield a peak time of 2 seconds and a 2% settling time of 10 seconds, and then calculate the resultant natural frequency and damping ratio. 4- for D=1 N.m.s/rad, find K and J to yield 20% overshoot and a peak time of 2 seconds, and then calculate the resultant natural frequency and damping ratio. 5- for J=0.5 kg.m², find K and D to yield 5% overshoot and a peak time of 1 second, and then calculate the resultant natural frequency and damping ratio.

Given the torsional system shown below actuated by a step input torc T(t): T(O) O0) fro> K D 1- Write first the equation of motion, and then: 2- for K=2 N.m/rad, find J and D to yield 15% overshoot and a 2% settling time of 5 seconds, and then calculate the resultant natural frequency and damping ratio. 3- for K=2 N.m/rad, find J and D to yield a peak time of 2 seconds and a 2% settling time of 10 seconds, and then calculate the resultant natural frequency and damping ratio. 4- for D=1 N.m.s/rad, find K and J to yield 20% overshoot and a peak time of 2 seconds, and then calculate the resultant natural frequency and damping ratio. 5- for J=0.5 kg.m², find K and D to yield 5% overshoot and a peak time of 1 second, and then calculate the resultant natural frequency and damping ratio.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

Given the torsional system shown below actuated by a step input torc T(t):
TO) 00)
lll
fro>
K
D
1- Write first the equation of motion, and then:
2- for K=2 N.m/rad, find J and D to yield 15% overshoot and a 2%
settling time of 5 seconds, and then calculate the resultant natural
frequency and damping ratio.
3- for K=2 N.m/rad, find J and D to yield a peak time of 2 seconds and a
2% settling time of 10 seconds, and then calculate the resultant natural
frequency and damping ratio.
4- for D=1 N.m.s/rad, find K and J to yield 20% overshoot and a peak
time of 2 seconds, and then calculate the resultant natural frequency
and damping ratio.
5- for J=0.5 kg.m², find K and D to yield 5% overshoot and a peak time
of 1 second, and then calculate the resultant natural frequency and
damping ratio.

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