Introduction
1. Theoretical Aspects of the Damped Mass-Spring System: Review the basic concepts of a mass-
spring system with damping in one dimension, where friction is modeled as a damping force
$F_d = \beta v$, with $\beta$ as the damping coefficient and $v$ the velocity. This approach represents real-
world systems where energy dissipation occurs, such as in mechanical systems with friction.
2. Importance in Engineering: This model applies to various engineering systems where oscillatory
motion and energy dissipation are crucial, including automotive suspension systems, building
structural engineering for seismic resistance, and shock absorption designs.
3. Applications and Relevance: Understanding damped oscillations allows engineers to design
systems with desired damping characteristics to control oscillatory responses, enhancing system
stability and longevity. Such systems are commonly used in suspension design, vibration
isolation, and in predicting material responses to oscillatory forces.
Instructions:
Part 1: MATLAB Function Development - MasaResorte()
1. Function Requirements: Create a MATLAB function MasaResorte() that takes in:
• Mass $m$
• Spring constant $k$
• Damping coefficient $\beta$
• Initial position $x_0$
• Initial velocity $v_0$
The function should return:
• Graphs of position, velocity, and acceleration as functions of time
• An indication of the type of motion: over-damped, critically damped, or under-damped.
2. Implementation Guidance:
• Use ode45 as the preferred solver for solving the second-order differential equation,
transforming it into a system of first-order equations.
• The solution should span a time vector appropriate to observe the system's decay behavior.
3. Plotting Requirements:
• Label axes on each graph to specify position (x), velocity (v), and acceleration (a) against
time.
