## Math 1060 – Trignometry

**Model of a Mass Spring System – Click here**

The mass spring system is used quite commonly in various applications all around us. Some examples would be Bungee jumping, a vehicle’s suspension and the landing wheels of the plane (landing gear). This aids us in understanding the motion of an object can be using trigonometry. The amplitude would determine how far up and down the motion of a mass-spring system will cause an object to rise or fall. The period can determine the length of time the object is in motion or the amount of time it takes for an object in motion to complete a full cycle. The frequency is how quickly the object in motion will move between its different phases. Frequency can be related to the vibration of an object and how quickly it would recoil.

In a car’s suspension the stiffness of the spring in the shock absorbers determines how smooth the car rides. A car moving on a bump at a certain speed with a softer spring will have a larger amplitude and longer period. This would result in a car with a soft ride. A car going over a bump at the same speed with stiff springs would have a smaller amplitude and shorter period. The stiffness of the spring is determined by the load of the vehicle. A load bearing vehicle has a stiffer spring in its suspension. Landing gear on a plane has a huge spring that acts as a shock absorber as well.

Knowing a lot of math and physics goes into building something is vastly different from actually understanding the math and physics working behind the scenes. This project brought to the forefront ideas that have never crossed my mind before. It makes one realize that simple things that we often take for grant have a lot more happening behind.