### Text Explanation:**Problem 3.44**: The landing gear of an airplane can be idealized as a spring-mass-damper system as shown in Figure 3.52. If the runway surface is described by \( y(t) = y_0 \cos \omega t \), determine the values of \( k \) and \( c \) that limit the amplitude of vibration of the airplane \( x(t) \) to 0.1 m. Assume \( m = 2000 \, \text{kg} \), \( y_0 = 0.2 \, \text{m} \), and \( \omega = 157.08 \, \text{rad/s} \).### Diagram Explanation:#### Figure (a):- **Depiction**: Front view of an airplane indicating the landing gear on the runway.- **Labels**: - Mass of the aircraft, \( m \), supported by the landing gear. - Wheels in contact with the ground. - A housing structure containing strut and viscous damping components.#### Figure (b):- **Schematic**: Represents the dynamic model of the landing gear system.- **Elements**: - **Mass (\( m \))**: Represents the aircraft's mass. - **Spring (\( k \))**: Shows the spring element in the suspension system. - **Damper (\( c \))**: Represents the damping component. - **Runway Surface**: Modeled as a sinusoidal wave \( y(t) \), indicative of surface undulations affecting the system. - **Output Motion**: Vertical displacement \( x(t) \) of the aircraft mass in response to runway surface irregularities. This setup is used for understanding the mechanical dynamics of how the landing gear responds to runway imperfections, crucial for minimizing the uncomfortable vibration during aircraft landing. Use \( k = 6 \times 10^6 \, \text{N/m} \).

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3.44 The landing gear of an airplane can be idealized as the spring-mass-damper system shown in Fig. 3.52 [3.16]. If the runway surface is described y(t) = y cos wt, determine the values of k and c that limit the amplitude of vibration of the airplane (x) to 0.1 m. Assume m = 2000 kg, yo = 0.2 m, and @ = 157.08 rad/s. pos y(t) x(t) H m (b) Wheel Runway Housing with strut and viscous damping Mass of aircraft, m to

3.44 The landing gear of an airplane can be idealized as the spring-mass-damper system shown in Fig. 3.52 [3.16]. If the runway surface is described y(t) = y cos wt, determine the values of k and c that limit the amplitude of vibration of the airplane (x) to 0.1 m. Assume m = 2000 kg, yo = 0.2 m, and @ = 157.08 rad/s. pos y(t) x(t) H m (b) Wheel Runway Housing with strut and viscous damping Mass of aircraft, m to

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

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Question

### Text Explanation:

**Problem 3.44**: The landing gear of an airplane can be idealized as a spring-mass-damper system as shown in Figure 3.52. If the runway surface is described by \( y(t) = y_0 \cos \omega t \), determine the values of \( k \) and \( c \) that limit the amplitude of vibration of the airplane \( x(t) \) to 0.1 m. Assume \( m = 2000 \, \text{kg} \), \( y_0 = 0.2 \, \text{m} \), and \( \omega = 157.08 \, \text{rad/s} \).

### Diagram Explanation:

#### Figure (a):
- **Depiction**: Front view of an airplane indicating the landing gear on the runway.
- **Labels**:
- Mass of the aircraft, \( m \), supported by the landing gear.
- Wheels in contact with the ground.
- A housing structure containing strut and viscous damping components.

#### Figure (b):
- **Schematic**: Represents the dynamic model of the landing gear system.
- **Elements**:
- **Mass (\( m \))**: Represents the aircraft's mass.
- **Spring (\( k \))**: Shows the spring element in the suspension system.
- **Damper (\( c \))**: Represents the damping component.
- **Runway Surface**: Modeled as a sinusoidal wave \( y(t) \), indicative of surface undulations affecting the system.
- **Output Motion**: Vertical displacement \( x(t) \) of the aircraft mass in response to runway surface irregularities.

This setup is used for understanding the mechanical dynamics of how the landing gear responds to runway imperfections, crucial for minimizing the uncomfortable vibration during aircraft landing.

Use \( k = 6 \times 10^6 \, \text{N/m} \).

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