Consider the following pendulum that consists of a massless straight rigid rod AOB with a point mass m attached at the top point B and a point mass M attached at the bottom point A. The pendulum rotates without friction about point O and it is initially at vertical equilibrium. Two springs are attached at the top point B from one end and fixed at the other end. The springs are unstretched at t=0 and the pendulum is vertical. 1. Find the linearized equation of motion of the pendulum with respect to the angle e from the rotation point O assuming small displacements from the vertical equilibrium position. 2. Find the natural frequency w, of the motion. 3. Find the rotational motion 8(t) for a given initial condition 4. Under what condition the linearized response is stable? O(0= 0, at rest. 2a Massless

Consider the following pendulum that consists of a massless straight rigid rod AOB with a point mass m attached at the top point B and a point mass M attached at the bottom point A. The pendulum rotates without friction about point O and it is initially at vertical equilibrium. Two springs are attached at the top point B from one end and fixed at the other end. The springs are unstretched at t=0 and the pendulum is vertical. 1. Find the linearized equation of motion of the pendulum with respect to the angle e from the rotation point O assuming small displacements from the vertical equilibrium position. 2. Find the natural frequency w, of the motion. 3. Find the rotational motion 8(t) for a given initial condition 4. Under what condition the linearized response is stable? O(0= 0, at rest. 2a Massless

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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Please find the question attached.

Consider the following pendulum that consists of a massless straight rigid rod
AOB with a point mass m attached at the top point B and a point mass M
attached at the bottom point A. The pendulum rotates without friction about point
O and it is initially at vertical equilibrium. Two springs are attached at the top
point B from one end and fixed at the other end. The springs are unstretched at
t=0 and the pendulum is vertical.
1. Find the linearized equation of motion of the pendulum with respect to the
angle e from the rotation point O assuming small displacements from the
vertical equilibrium position.
2. Find the natural frequency w, of the motion.
3. Find the rotational motion 8(t) for a given initial condition
4. Under what condition the linearized response is stable?
O(0= 0, at rest.
2a
Massless

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