A measurement device is constructed from two (identical) uniform bars, welded together at right angles and pivoted about a horizontal axis through point O as illustrated in Figure Q3. Each of the bars has mass m, and each end of the horizontal bar is supported by identical springs, each of stiffness k, and both of which are connected to a solid surface. A torsional damper with damping coefficient, ce, is applied at the pivot at O. A horizontal force of magnitude F (t) = 4.59e¬t, (where t is the time in seconds), is now applied to the end of the vertical bar as illustrated, causing the system to rotate. Q3 (a) Show that the moment of inertia of the welded bars about the pivot O is given by ml?. 12 (b) Assuming that neither spring is extended when the system is stationary, find the equation of motion of the system. (c) The system has the following properties: k = 81.5 N/m; L=56 cm; Ce = 0.79 Nms/rad ; т — 780 grammes With the force, F(t), as given above, determine if the system is sub-critically damped or overdamped, and determine the natural frequency of oscillation, Wn. (d) Using a Laplace Transform approach, determine the response of the system, e(t), to the applied force, F(t). You may assume that gravitational acceleration, g = 9.81 m/s², and that the small angle approximation may be used throughout. L/2 L/2 0 +ve
A measurement device is constructed from two (identical) uniform bars, welded together at right angles and pivoted about a horizontal axis through point O as illustrated in Figure Q3. Each of the bars has mass m, and each end of the horizontal bar is supported by identical springs, each of stiffness k, and both of which are connected to a solid surface. A torsional damper with damping coefficient, ce, is applied at the pivot at O. A horizontal force of magnitude F (t) = 4.59e¬t, (where t is the time in seconds), is now applied to the end of the vertical bar as illustrated, causing the system to rotate. Q3 (a) Show that the moment of inertia of the welded bars about the pivot O is given by ml?. 12 (b) Assuming that neither spring is extended when the system is stationary, find the equation of motion of the system. (c) The system has the following properties: k = 81.5 N/m; L=56 cm; Ce = 0.79 Nms/rad ; т — 780 grammes With the force, F(t), as given above, determine if the system is sub-critically damped or overdamped, and determine the natural frequency of oscillation, Wn. (d) Using a Laplace Transform approach, determine the response of the system, e(t), to the applied force, F(t). You may assume that gravitational acceleration, g = 9.81 m/s², and that the small angle approximation may be used throughout. L/2 L/2 0 +ve
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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QUESTIION A. B AND C
Transcribed Image Text:A measurement device is constructed from two (identical) uniform bars,
welded together at right angles and pivoted about a horizontal axis through
point O as illustrated in Figure Q3. Each of the bars has mass m, and each end
of the horizontal bar is supported by identical springs, each of stiffness k, and
both of which are connected to a solid surface. A torsional damper with
damping coefficient, co, is applied at the pivot at O. A horizontal force of
magnitude F(t) = 4.59e-t, (where t is the time in seconds), is now applied to
the end of the vertical bar as illustrated, causing the system to rotate.
Q3
(a)
Show that the moment of inertia of the welded bars about the pivot O is given
5
byml?.
12
(b)
Assuming that neither spring is extended when the system is stationary, find
the equation of motion of the system.
(c)
The system has the following properties:
k 3D 81.5 N/т; L%3D 56 ст;
Ce = 0.79 Nms/rad ;
т 3D 780 grammes
With the force, F(t), as given above, determine if the system is sub-critically
damped or overdamped, and determine the natural frequency of oscillation,
Wn.
(d)
Using a Laplace Transform approach, determine the response of the system,
O (t), to the applied force, F(t)
9.81 m/s², and that the
You may assume that gravitational acceleration, g
small angle approximation may be used throughout.
L/2
L/2
0 +ve
k
k
Figure Q3.
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