2. In the system shown in Figure 2, the massless rigid rod of length l =4 +½ is pivoted at point P. A mass m is attached to one end of the rod, while two identical springs are attached to the other end of the rod. The displacement x is measured from the equilibrium position. Assuming that x is small, find the equation of motion and the natural frequency of the system using the energy method. The image depicts a mechanical system diagram labeled as Figure 2. It features a mass-spring arrangement as described below:- A mass, labeled \( m \), is positioned on a rigid beam.- The beam is supported at a pivot point, marked as \( p \), and extends to a point at the opposite end of the pivot.- Two lengths are shown from the pivot \( p \): - \( l_1 \) is the distance from the mass \( m \) to the pivot \( p \). - \( l_2 \) is the distance from the pivot \( p \) to the endpoint connected to springs.- Two springs, each with a spring constant \( k \), are attached to the beam's endpoint opposite the mass.- These springs are mounted vertically between a fixed support at the top and a fixed base at the bottom.- A displacement variable, \( x \), is indicated at the point where the springs connect to the beam.This diagram can represent a dynamic system where the beam can oscillate around the pivot \( p \) while compressing and extending the springs.

Answered: Image /qna-images/answer/8da91abb-79b5-4a2a-b655-8059b104d682.jpg

Answered: 4. m. Figure 2

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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2. In the system shown in Figure 2, the massless rigid rod of length l =4 +½ is pivoted at point P. A mass m is attached to one end of the rod, while two identical springs are attached to the other end of the rod. The displacement x is measured from the equilibrium position. Assuming that x is small, find the equation of motion and the natural frequency of the system using the energy method.

The image depicts a mechanical system diagram labeled as Figure 2. It features a mass-spring arrangement as described below:

- A mass, labeled \( m \), is positioned on a rigid beam.
- The beam is supported at a pivot point, marked as \( p \), and extends to a point at the opposite end of the pivot.
- Two lengths are shown from the pivot \( p \):
- \( l_1 \) is the distance from the mass \( m \) to the pivot \( p \).
- \( l_2 \) is the distance from the pivot \( p \) to the endpoint connected to springs.
- Two springs, each with a spring constant \( k \), are attached to the beam's endpoint opposite the mass.
- These springs are mounted vertically between a fixed support at the top and a fixed base at the bottom.
- A displacement variable, \( x \), is indicated at the point where the springs connect to the beam.

This diagram can represent a dynamic system where the beam can oscillate around the pivot \( p \) while compressing and extending the springs.

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