Question

13. Briefly describe how a two degree of freedom system can be made to vibrate in one of its pure modes. sャ 2. (a) Sketch the amplitude ratio and phase angle for damping of 0.01 and 0.3, and indicate the peak amplitude values. Name the axes with correct numerica (b) Compare this amplitude diagram with a similar one that corresponds to base excitation, emphasizing t a single degree of freedom system subjected to harmonic force with phasizing the differences (15)

Answer 1

Ans 13 :

Systems that require two independent coordinates to describe their motion are called two degree of freedom systems, There are two equations for a two degree of freedom system, one for each mass (precisely one for each degree of freedom).

They are generally in the form of coupled differential equations‐that is, each equation involves all the coordinates.If a harmonic solution is assumed for each coordinate,the equations of motion lead to a frequency equation that gives two natural frequencies of the system.If we give suitable initial excitement on, the system vibrates at one of these natural frequencies. During free vibration at one of the natural frequencies, the amplitudes of the two degrees of freedom (coordinates) are related in a specified manner and the configuration is called a normal mode, principle mode, or natural mode of vibration.