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Homework answers / question archive / Project 3_2 Fall 2022 The measured natural frequency and damping ratio of the spring mass damper (M1 K1 C1), dubbed ‘structure’ shown in the figure are 1

Project 3_2

Fall 2022

The measured natural frequency and damping ratio of the spring mass damper (M1 K1 C1), dubbed ‘structure’ shown in the figure are 1.1 Hz and 1%, respectively. The mass M1, weighing 60 lbs, is subject to a perturbing force.

1. Model the structure and derive the transfer function with the force perturbing the mass M1 as the input and the acceleration of M1 as the output.

2. Using your model derived in part 1, plot

a. the unit impulse response, and

b. the frequency response

of the structure.

3. To lower the vibration of the mass M1, it is suggested to add append a pendulum tuned to the natural frequency of the structure, to the structure.

a. What is the number of degrees of freedom of the structure+pendulum

b. Repeat part 1, i.e., derive the transfer function with the force perturbing the mass M1 as the input and the acceleration of M1 as the output. Use the following to find the parameters of the pendulum:

i. mass ratio M2/M1=0.05 (or 5%),

ii. damping ratio ?2=15% (for the pendulum),

iii. tuning the pendulum to the natural frequency of the structure means ?n2=0.97*?n1.

4. Using the model of part 3-b, repeat parts 2-a and 2-b. Make sure the plots of part 4 are placed on the same coordinates as those of parts 2-a and 2-b

5. Elaborate on the impact of adding the pendulum to the structure.

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