Question

6. An underdamped shock absorber for a moon-buggy is to be designed. The system can be considered as simple SDOF system weighing 2500 N as shown in Figure 2 (a) and its damped free vibration response is shown in Figure 2 (b).lf the damped period of vibration is to be 0.8 sec and the amplitude x, is to be reduced to one-third in one half cycle. A/2 a. Draw the free-body and kinetic diagrams for the system. b. Determine the logarithmic decrement from the response. c. Find the damping ratio using the logarithmic decrement d. Obtain the undamped and damped natural frequencies of the unit. e. Estimate the spring constant and damping coefficient of the system.

Answer 1

mu (a) FBD the 2 u2y s hs 2. damper Foice dis placemen at XI end ofFirst oscilation when EwnTd X e - sinp one and halF displacement and end X2= 0scillatisn whon -Cn3Td sinp X e Ewn Td Xi X 2 (1.5-1) EwnT . e. wnTel X2

X2= egasthmic decrement n3 E wnTd 2 2 A E n 2 2.1932 - E2 - 2.5 E O 33 2 7 2 7 = 7.0 5 7/s O.a Td on = i- o-33 2

e 2 2. (8-316) K = 9.81 17 624 KN m 2K O 33 2 25D 17.624X1 9.01 2 X.33 449133 5372 N/m/s 398.723 1 0