Consider the below system which is vibrating with sinusoidal input of ?in (38.88?) ?. The damping coefficient of the system is experimentally calculated to be 0.5 ?. ?/?. We locate mass ?₂ along the beam as tuned-mass-damper (TMD) at distance ?₂ from origin to deal with the vibration of ?₁ = 0.15 ?g, which is located at ?₁ = 0.25 ? from origin. Investigate how much, percentage of the maximum displacement of ??1 could be reduced during the steady state vibration. The modulus of elasticity of the steel ruler is ? = 210 ?Pa and width and thickness of the ruler are 20 mm and 1.5 mm, respectively.

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(a) Demonstrate how much the vibration of m 1 could be changed with comparisons of the maximum
displacement during the steady state vibration with TMD (locating in: = 0.1 kg at L2 = 0.536 m)
compared to without TMD. (b) Plot the position (mm) versus time (s) graphs of ml within 20... 

Please provide me step by step answers with a Matlab file which includes simulation, plots and reports.