* = Seen in Figure 1, a rotating mass (with mass moment of inertia Id = to a fixed wall (on the far left) by a torsional spring (k 1kg m² and angular position a) is attached 1Nm/rad) and a torsional damper. Consider the spring and damper as concentric and in parallel. Dampers with damping ratios of c = be considered. At t = 0, a unit step torque Tin is applied to the rotating mass. A unit step input is a forcing function - 0.1, 0.5, 1.0, and 1.5kg m²/s will whose value is 0 from -∞ to some time to and 1 from to to co. Here, to = 0. k minning C 0 doc la Tin 0d *

* = Seen in Figure 1, a rotating mass (with mass moment of inertia Id = to a fixed wall (on the far left) by a torsional spring (k 1kg m² and angular position a) is attached 1Nm/rad) and a torsional damper. Consider the spring and damper as concentric and in parallel. Dampers with damping ratios of c = be considered. At t = 0, a unit step torque Tin is applied to the rotating mass. A unit step input is a forcing function - 0.1, 0.5, 1.0, and 1.5kg m²/s will whose value is 0 from -∞ to some time to and 1 from to to co. Here, to = 0. k minning C 0 doc la Tin 0d *

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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Question

Seen in Figure 1, a rotating mass (with mass moment of inertia Id
to a fixed wall (on the far left) by a torsional spring (k
1kg* m² and angular position a) is attached
1Nm/rad) and a torsional damper. Consider the spring
and damper as concentric and in parallel. Dampers with damping ratios of c =
be considered. Att =
0.1, 0.5, 1.0, and 1.5kg * m²/s will
0, a unit step torque Tin is applied to the rotating mass. A unit step input is a forcing function
whose value is 0 from -∞o to some time to and 1 from to to oo. Here, to = 0.
Your tasks:
k
ww
+
C
=
la
Od
A Derive the equation of motion of the rotating mass. Write c as
EOM's for the different values of c.
Tin
0
Figure 1: Schematic of the mechanical system to model in Problem 1.
em, you will solve part B over MA AB Grader Plea
LO
onment
variable. You do not need to write separate
ד ו.
for

Expert Solution

Step 1: Given

The torsional spring is $k equals 1 space N m divided by r a d$ .

The moment of inertia is $I subscript d equals 1 space k g m squared$ .

The input torque is $T subscript i n end subscript$ .

The angular position is $theta subscript d$

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