# Free Vibration of Cantilever Beam with Lumped Mass at Free End

Questions

1. The theoretical natural frequency obtained is damped or undamped natural frequency?
2. The experimental natural frequency obtained is damped or undamped natural frequency?
3. What would be the effect on the natural frequency when a notch is cut on the cantilever beam?
4. Where the location of the notch would have effect on the natural frequency of the cantilever beam?
5. Do you think the sensor weight would affect the natural frequency of the beam?
6. What is the affect of damping on the natural frequency? Could you tell whether the obtained natural frequency is damped  natural frequency or undamped one?
7. What is the relationship between the damped and undamped natural frequencies?
8. Do you think the natural frequency and the damping ratio would change if we consider subsequent consecutive free vibration amplitudes instead of first two amplitudes?
9. Do you think the beam tightening at the support (i.e., the flexibility of support) would affect the natural frequency of the system?
10. What type of free vibration signal you would expect if the beam is given initial disturbance other than the free end (i.e., if the initial disturbance excites higher modes of vibration also)?
11. How many distinct natural frequencies can exist for an ‘ N’ degree of freedom vibratory system?
12. Is the frequency of a damped free vibration smaller or greater than the natural frequency of a system? Why?
13. What is the basic difference between the free responses exhibited by an under dampeds ystem and an over damped system?
14. For the system given in example 2.1, if we add a mass of 500k gm at free end then find  out the  natural frequency of that system?
15. How many number of degree of freedom has the given system if it is considered as discrete system with N number of masses in Fig 2.1?
16. A system has n mode shapes. Then how many numbers of natural frequencies the system has?
17. Do you think other boundary conditions (e.g., the simply supported beam, fixed-fixed, or free-free beam) have same natural frequency as fixed-free case (i.e. cantilever case)? Obtain the theoretical natural frequencies for such case of the present beam and compare with the present one.
18. Damped free oscillation amplitude is observed to be reduced to 20% of its initial amplitude in 100 complete cycles. Estimate the damping ratio ς.