Consider the dynamic system shown below.The diagram features a double pulley system with the following components:- Two radii, \( r_1 \) and \( r_2 \), are labeled on the pulley.- The pulley rotates around a fixed point \( O \) with an angular displacement \( \theta \).- A moment of inertia \( J_O \) is indicated around the point \( O \).- There are two springs attached to the system: - Spring with stiffness \( k_2 \) is connected to a wall and \( r_2 \) on the pulley. - Spring with stiffness \( k_1 \) is connected between the mass \( M \) and \( r_1 \) on the pulley.- The mass \( M \) is connected to the spring \( k_1 \) and can move vertically, indicated by the displacement \( x \).Determine the characteristic equation(s) when a torque equal to \( \tau(t) \) is applied to the double pulley.

Determine the characteristics equation?

Answered: Consider the dynamic system shown…

Consider the dynamic system shown below. Jo k₂ M Determine the characteristic equation(s) when a torque equal to r(t) is applied to the double pulley.

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 undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

Consider the dynamic system shown below.

The diagram features a double pulley system with the following components:

- Two radii, \( r_1 \) and \( r_2 \), are labeled on the pulley.
- The pulley rotates around a fixed point \( O \) with an angular displacement \( \theta \).
- A moment of inertia \( J_O \) is indicated around the point \( O \).
- There are two springs attached to the system:
- Spring with stiffness \( k_2 \) is connected to a wall and \( r_2 \) on the pulley.
- Spring with stiffness \( k_1 \) is connected between the mass \( M \) and \( r_1 \) on the pulley.
- The mass \( M \) is connected to the spring \( k_1 \) and can move vertically, indicated by the displacement \( x \).

Determine the characteristic equation(s) when a torque equal to \( \tau(t) \) is applied to the double pulley.

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