Why Do Vibrations Slowly Die Out? | 30 Day MATLAB Challenge #6

Why don’t vibrating systems oscillate forever?

In Day 6 of my 30 Day MATLAB Challenge, I explored the spring–mass–damper system and simulated damped oscillatory motion using MATLAB.

Using vibration equations, damping ratios, and exponential decay models, I visualized how oscillations gradually reduce in amplitude over time.

📌 Topics Covered:
• Spring–mass–damper systems
• Natural frequency
• Damping ratio
• Damped natural frequency
• Oscillatory motion
• Exponential decay envelopes
• MATLAB visualization of vibrations

📚 Governing Equation:

mẍ + cẋ + kx = 0

📚 Key Equations Used:

ωₙ = √(k/m)

ζ = c / (2√mk)

ω_d = ωₙ√(1 − ζ²)

x(t) = x₀e^(-ζωₙt) cos(ω_dt)

🛠️ Tools Used:
MATLAB R2026a

This series is my attempt to learn MATLAB through Mechanical Engineering concepts and computational simulations — one project at a time.

#MATLAB #MechanicalEngineering #Vibrations #Dynamics #EngineeringStudent #ControlSystems

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