Equation (2.1) is obtained by normalising the following differential equation. Normalising in this case implies dividing through by the mass of the vehicle. 

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m-Mass of the vehicle 

k-Spring constant 

c-Dampening constant 

α-Displacement at any time t. 

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A harmonic system utilises principles such as Hooke's Law to simulate a uniform force applied to the system as a result of the spring constant, k.

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The equation  

Equation 2.1.1 Divided through by mass gives 

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The solution to the differential equation (2.1) is equation (2.2). The system is underdamped hence the roots are complex. The general solution would be: 

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It is mathematically proven that the angel ∅ is equal to 0.∅ is equal to 0.

 

Differentiating equation (2.2), displacement gives equation (2.3), velocity. The derivative of equation (2.3) results into equation (2.4) which is acceleration. 

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