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MEC524 — Chapter 3
Mathematical Modeling
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Mechanical Building Blocks

Mass, spring, and damper are the three fundamental elements of all mechanical system models. Every translational or rotational system can be decomposed into combinations of these building blocks, each with a distinct energy role.

◆ Diagram
Mechanical Building BlocksMassmFaProperty: InertiaF = m·aStores Kinetic EnergySpringkxProperty: StiffnessF = k·xStores Potential EnergyDampercProperty: FrictionF = c·ẋDissipates as HeatEquation of Motionmẍ + cẋ + kx = F(t)The three fundamental physical elements of mechanical systems
◆ Key Points
01.Mass (m): inertia — stores kinetic energy, F = ma
02.Spring (k): stiffness — stores potential energy, F = kx
03.Damper (c): friction — dissipates energy as heat, F = cv
04.These three elements form the basis of all mechanical system models
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