In this video, we study the vibration of a special case of two degree of freedom systems which is the vibration of semi-definite systems. Semi-definite systems are also known as unrestrained or degenerate systems which show a very interesting behavior different from regular systems. The natural frequency for the first mode shape of such systems is zero which means that the first mode shape does not harmonically change by time and acts like a rigid body motion of the two masses together without any relative motion with respect to each other. Note that the total response of each degree of freedom in such systems is the summation of the two mode shapes which then includes the harmonic term from the second mode shape with a non-zero natural frequency. The semi-definite systems exist on both translational and rotational motions, and here we show a simple translational motion example.
#unrestrained_or_degenerate_systems
#two_degree_of_freedom_systems
#Semi_Definite_Systems
#Natural_frequency
#Mode_shape
#non_zero_natural_frequency
#Harmonic_Term
#Translational_Motion
#Rotational_Motion
#Vibration_System
#Mechanical_Vibration
#Rigid_Body
#Second_Mode
#Undergraduate_Vibration
#Vibration_Course
