Understanding Vibration and Resonance

thanks to curiositystream for sponsoring this video a good understanding of how structures behave when vibrating is what allows engineers to build rotating machinery to launch sensitive instruments into space and to safely design buildings and seismic areas to name just a few of the many applications systems like these can be very complex so to study their vibrating behavior

engineers usually start by building a simple model that approximates the dynamics of the system but is easier to assess the two most important parameters in any vibrating system are its mass and its stiffness a common modeling approach is to lump all the different contributions to mass and stiffness together and represent them using a point mass with a mass m

and a spring with a stiffness k this is called the lumped parameter modeling approach this kind of simplified model might seem quite abstract but can actually represent the dynamic behavior of a lot of real systems quite accurately the beauty of this simplicity is that we now have something that we can analyze mathematically but first we have to make

a few assumptions we'll assume that the mass can only move up and down since the system behavior is defined by a single output the x-coordinate of the mass this is what's called a single degree of freedom model we'll also neglect the effects of gravity and for now we'll assume that there's no damping meaning that no

energy is lost from the system as it vibrates by friction or other means no external loads are acting on the system the purpose of the model is to understand how the system behaves in free vibration or in other words how it will oscillate when it's displaced and then released since we've assumed there's no damping the mass will