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**Solving Engineering Problems in Dynamics**

Michael Spektor

171 Pages, Softcover

Published: April, 2014

*Solving Engineering Problems in Dynamics* helps practicing engineers successfully analyze real mechanical systems by presenting comprehensive methods for analyzing the motion of engineering systems and their components. This analysis covers three basic phases: 1) composing the differential equation of motion; 2) solving the differential equation of motion; and 3) analyzing the solution. Although a formal engineering education provides the fundamental skills for completing these phases, many engineers nonetheless would benefit by gaining further insight in using these fundamentals to solve real-life engineering problems. This book thus describes in step-by-step order the methods related to each of these phases.

Features

- A basic education in engineering is sufficient to master the contents of this guide and effectively apply its step-by-step methods for solving engineering problems.
- Numerous solutions of examples of linear, non-linear, and two-degree-of-freedom systems are found throughout.
- Explains the structures of differential equations of motion of the two-degree-of-freedom systems and demonstrates the applicability of the Laplace Transform methodology for solving these equations.
- Many types of engineers can benefit from this book (as well as students in mechanical, manufacturing, and industrial engineering).

TOC

**Introduction**

**Differential Equations Of Motion**

- Analysis Of Forces
- Analysis of Resisting Forces
- Forces of Inertia
- Damping Forces
- Stiffness Forces
- Constant Resisting Forces
- Friction Forces
- Analysis of Active Forces
- Constant Active Forces
- Sinusoidal Active Forces
- Active Forces Depending on Time
- Active Forces Depending on Velocity
- Active Forces Depending on Displacement

**Solving Differential Equations of Motion Using Laplace** **Transforms**

- Laplace Transform Pairs For Differential Equations of Motion
- Decomposition of
** **Proper Rational Fractions
- Examples of Decomposition of Fractions
- Examples of Solving Differential
** **Equations of Motion
- Motion by by Inertia with no Resistance
- Motion by Inertia with Resistance of Friction
- Motion by Inertia with Damping Resistance
- Free Vibrations
- Motion Caused by Impact
- Motion of a Damped System Subjected to a Tim Depending Force
- Forced Motion with Damping and Stiffness
- Forced Vibrations

**Analysis of Typical Mechanical Engineering Systems**

- Lifting a Load
- Acceleration
- Braking
- Water Vessel Dynamics
- Dynamics of an Automobile
- Acceleration
- Braking
- Acceleration of a Projectile in the Barrel
- Reciprocation Cycle of a Spring-loaded Sliding Link
- Forward Stroke Due to a Constant Force
- Forward Stroke Due to Initial Velocity
- Backward Stroke
- Pneumatically Operated Soil Penetrating Machine

**Piece-Wise Linear Approximation**

- Penetrating into an Elasto-Plastic Medium
- First Interval
- Second Interval
- Third Interval
- Fourth Interval
- Non-linear Damping Resistance
- First Interval
- Second Interval

**Dynamics of Two-Degree-of-Freedom Systems**

- Differential Equations of Motion: A Two-Degree-of-Freedom System
- A System with a Hydraulic Link (Dashpot)
- A System with an Elastic Link (Spring)
- A System with a Combination of a Hydraulic Link (Dashpot) and an Elastic Link (Spring)
- Solutions of Differential Equations of Motion for Two-Degree-of-Freedom Systems
- Solutions for a System with a Hydraulic Link
- Solutions for a System with an Elastic Link
- Solutions for a System with a Combination of a Hydraulic and an Elastic Link
- A System with a Hydraulic Link where the First Mass Is Subjected to a Constant External Force
- A Vibratory System Subjected to an External Sinusoidal Force