Answered: An underdamped shock absorber is to be…

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

See similar textbooks

Related questions

Concept explainers

Question

An underdamped shock absorber is to be designed for a motor cycle of mass 200 kg(m). When the shock absorber is subjected to an initial vertical velocity due to a road bump, the resulting displacement-time curve is to be as indicated below. Find the necessary stiffness and damping constants of the shock absorber if the damped period of vibration is to be 10 sec(τd) and the amplitude x1is to be reduced to one-eighth in one half cycle. Example is attached

**Example 2-14: Shock Absorber for a Motorcycle**

An underdamped shock absorber is to be designed for a motorcycle of mass 200 kg (m). When the shock absorber is subjected to an initial vertical velocity due to a road bump, the resulting displacement-time curve is to be as indicated below. Find the necessary stiffness and damping constants of the shock absorber if the damped period of vibration is to be 2 sec (τd) and the amplitude x1 is to be reduced to one-fourth in one half cycle (i.e., \(x_{1.5} = \frac{x_1}{4}\)).

**Diagram:**

- The diagram shows a motorcycle wheel with an attached shock absorber system. The system is depicted as a spring and damper (k/2, b/2) representing half-spring and half-damping coefficients, respectively.
- The displacement over time curve is plotted, showing \(x(t)\) with decreasing amplitudes x1, x1.5, and x2.5 over time.

**Equations:**

1. \(x_{1.5} = \frac{x_1}{4}\), \(x_2 = \frac{x_{1.5}}{4} = \frac{x_1}{16}\), ... leading to
\[
\delta = \ln \left( \frac{x_1}{x_2} \right) = \ln(16) = 2.7726 = \frac{2\pi \zeta}{\sqrt{1-\zeta^2}} \rightarrow \zeta = 0.4037
\]

2. Damping ratio (ζ) is calculated using the equation
\[
\delta = \frac{2\pi \zeta}{\sqrt{1-\zeta^2}}
\]

3. \(τ_d = \frac{2\pi}{ω_d}\) leads to \(ω_d = π\).
\[
ω_d = ω_n \sqrt{1-\zeta^2} = π \rightarrow ω_n = \frac{π}{\sqrt{1-(0.4037)^2}} = 3.4338 \, \text{rad/sec}
\]

4. Natural frequency (\(ω_n\)) is calculated as:
\[
ω_n = \sqrt{\frac{k

Expert Solution

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions