 |
Physical Meaning of Normal Modes (contd….) |
| |
In the first mode of vibration, both the masses have the same amplitude and hence the middle spring is undeformed. Hence we can ignore the presence of this spring and each spring-mass system is operating independently. Hence the natural frequency is same as a simple spring-mass SDOF system i.e. |
| |
In the second mode of vibration, the two masses are exactly out of phase i.e. the two ends of the intermediate spring move by the same amount in opposite directions. Thus the mid-point of the intermediate spring will be at rest and hence we can consider the intermediate spring to be cut into two and arrested at the middle as shown in Fig. 10.1.4 below. We know that when a spring is cut into two, its stiffness is doubled and when twosprings are in parallel, their stiffnesses add up. Thus the equivalent system is as shown in the figure. Thus the natural frequency is given by: |
| |
|
| |
Which is same as what we got by solving the two d.o.f system equations.
|
