Harmonic Motion in Car Shock Absorber

Did you realize that frequently repeating movements and waves in any of their complexity, may be considered as a chain of simple harmonic movements or the sum of waves? The first scientist who discovered this discovery was Joseph Fourier, a French mathematician who lived around 1822. In physics, a simple harmonic motion is a type of oscillation when the maximum displacement of one side equals the maximum displacement of the other side. It is defined by repetitive back-and-forth motion through an equilibrium or middle point. The time interval is the same for every complete swing. Movement is always caused by a force that is directly proportionate to the distance from the equilibrium point and is always directed toward that position.

 The typical equation for this movement is   F = -kx, which is based on Hooke's law. F is the force, x is the displacement, and k is the constant in this equation. However, Newton's second law (F = ma) can be applied and set as ma = -kx to specify how the displacement of a mass changes over time. The resulting differential equation can be solved as x = A cos ωt, where acceleration, a is the second derivative of x with respect to time, t, and where ω is the angular frequency in radians per second and A is the maximum displacement. The time it takes mass to travel from point A to point -A and back is equal to the time it takes " ωt" to travel by 2π. Then, ωT = 2π or T = 2π /ω is the period required for a mass to go from A to -A or vice versa.

 With simple harmonic motion, no energy dissipation mechanism causes an object to vibrate with the same amplitude. But friction or other mechanisms of energy dissipation are always present. The amplitude ofthe oscillation reduces with time in the presence of energy dispersion or dissipation, and the motion can no longer be represented as a simple harmonic motion. Rather, it's known as damped harmonic motion, and the amplitude drop is referred to as "damping."

 One of the most well-known applications for damped harmonic motion is the automotive suspension system. A shock absorber connected to the main spring of a vehicle suspension is visualized in Figure 1. Shock absorbers are meant to lessen vibrations caused by bumpy rides by creating dampening forces. The shock absorber is made up of a piston in the oil reservoir, as shown in portion b of the diagram. Holes in the piston head allow oil to travel through the piston when it moves in reaction to the bumpy road surfaces. Damping is caused by the viscous force exerted by this movement.

Figure 1 shows simplified cross-sectional views of (a) a shock absorber installed in a vehicle's suspension system and (b) a shock absorber.

Authors: Amir Syakir, Muhammad Syafi, Muhammad Afiq & Gs. Dr. Ya’akob Mansor

Tarikh Input: 20/12/2023 | Kemaskini: 20/12/2023 | emma