please solve! sos 35404550-556065-70-7580110100Omega rad/s (eo)Fig. 2aData pertaining to X1/F1 can be found in BeachBoard file: X1_F1_FRF.txtFrequency Response Function X,/F,-5055-60-70-75-801.00omegtPRIys (m)100.00Fig. 2BData pertaining to X2/Fz can be found in BeachBoard file: X2_F2_FRF.txtdB ref 1 MAE 376 Fall 2021 ProjectM,= 5kgM,= 7kg(K2)1=700 N/m case 1c:=0 F;=F;=0c,=0 F;=F;=0(K2)2 = 5000 N/m case 2wwimwwwmm2Figure 1. Two-degree of freedom Duffing oscillator.1) Fig. 2a and Fig. 2b show the Frequency Response Function (FRF) X1/F1 andX2/F2 respectively. The data related to these can be found in BeachBoard.This experimental data pertains to case 1 (k2=700 N/m). Since this is a weakconnection, the frequencies pertaining to the peaks in the graphs are goodestimates to the natural frequencies (@n) of_- and. Apply the half-power-bandwidth method to estimate the damping factors ,(use data X1/F1)and 53 (use data X2/F2).2) Using Simulink, create a block diagram corresponding to Figure 1. Apply aninitial displacement of 0.1m on m2. Plot the displacements (with respect totime 0-10s) of m and m2. Solve for case 1 and case 2.3) Calculate and plot the Frequency Response Function (FRF) for X1/F1 for case2 (k2=5000 N/m). Compare the FRF with that of case 1. Can good estimatesand §, be estimated using case 2 data?msfor4) Set all of the damping, c's, to zero and derive the equation of motion byapplying Lagrange equation.

As per Bartleby terms and conditions we are restricted to solve only one question at a time . yor are requested to post other question separtly . Thank you . Solving question no 1) Natural frequency for case 1 fn1=ωn12πfrom graph 1ωn1=24fn1=242π=3.8Hzf1=20/2π=3.18Hzf2=26/2π=4.13Hz Damping factor for case 1 ξ1=f1-f22fn1=3.18-4.132×3.8=-0.125 Natural frequency for case 2 fn2=ωn22πfrom graph 2ωn2=38fn2=38/2π=6.04Hzf1=30/2π=4.77Hzf2=45/2π=7.16Hz Damping factor for case 2 ξ2=f1-f22fn2=4.77-7.162×6.04=-0.197