MEEN 350 : Dynamic Systems and Vibration - Spring Force and Damper Force - MATLAB Assignment Help

Assignment Task :

PROBLEM:  

The dynamic system, shown in Figure 1, is given. The beam AOE is rigid but massless. The pivot point O is frictionless. The following parameters are given: m1=1 kg, m2=3 kg, C=5 N s/m, K=635 N/m, a=0.2 m, b=0.4 m, and d=0.3 m. 

(a) Derive the equation of the motion (ODE) using any method you desire. Leave the  force as F(t). Convert the ODE equation to state space form (x= Ax + Bu and y = Cx + Du). We need to plot the following parameters: θ, ω, spring force, and damper  force. Derive the A, B, C, and D matrices. What is the undamped natural frequency,  ωn, of this system? (20 points)  

(e) If the input force F(t) is equal to F(t) = 20 Sin (12.56t), to reduce θ at steady state, what vibration reduction method do you recommend that we should use?  Demonstrate or prove that your approach works.  

Format of the MATLAB report 

1) Cover page (use the provided cover page) 

2) Attach copy of the assignment (this page) 

3) Equations of the motion for system of Figure 1 and convert the ODEs to state space form

4) Attach hard copy of your M-file 

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