An elliptical hoop of negligible thickness witha vertical orientated semi-major axis a and ahorizontal orientated semi-minor axis b, whichhas a mass per unit length of p, is mountedon a circular peg to which is attached a Carte-sian xy coordinate system in a vertical orienta-tion as shown in the accompanying sketch (the gravity gellipse and peg are not rigidly joined to eachother and are simply in kinematic contact witheach other with negligible friction), such thatthe physical system lies within a flat xy plane.The ellipse is then allowed to freely oscillate ina to-and-fro rocking motion by a small angle 0,such that the gravitational accelerationacts9in a downwards direction that is parallel to theellipse semi-major axis.1.2a1.3bConsidering the above system determine the following information clearly showing all steps andappropriate reasoning:Y(Using the energy method (T+V) =const. where T is the kinetic energy and Vis the potential energy derive the underlying equation of motion for the systemby taking the angle as the independent variable that models the Single-Degree-of-Freedom (SDOF) vibration for the system;Utilizing the previously derived equation of motion determine the correspondingnatural angular frequency wn for the Simple Harmonic Motion (SHM) of thevibrating system;X

Name: An elliptical hoop of negligible thickness witha vertical orientated
Uploaded: 2024-03-20T06:56:55.000Z
Channel: Bartleby
Description: An elliptical hoop of negligible thickness witha vertical orientated semi-major axis a and ahorizontal orientated semi-minor axis b, whichhas a mass per unit length of p, is mountedon a circular peg to which is attached a Carte-sian xy coordinate sy