Question

EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k. Friction and any other dissipative terms are negligible. k Draw the free body diagrams for the two bodies. a) | y1 |F b) Write the equation of motion in matrix form, expressing the content of each matrix/vector m1 c) Calculate the natural frequencies of the system, knowing that m1 1 kg, m2 2 kg and k = 1000 N/m k d) Draw the mode shapes of the system Qualitatively draw the frequency response functions of x1 and x2 to e) the input F Fo cosît j The position in figure for y1-0 and y2=0 is an equilibrium position y2 m2

Answer 1

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333.33 r2 こ0 n 2 3 3 3.33 - 2 on 2 I666. 67 (33 3.33 2 2) xC66.6-w) 0こ(と)999|× 9999 Do t333.33wn 2 33 3.33 2 2 222 1.U 2 co E11 18.g9 2 2 +1000 nこ1333340 Divided b - 6 66 670 2 2 - 666670 co2 6 L6670 and co^t Q太999 0oSt 2 CUn Taking t6666 70 Cn Sqyare 66 610 Wn 816.498 Con 816-19 reguenci Wn 816.498 rad /sec n atura es Thesetore aTe Sysiem he Wn2- 1816.19 fadlsec and

The natural modes q sstem bor kirst mass. M m2w K. a 2 Mun O O o 2 -o oo o o o 1332337.96 7. SOSX n 2 2 x (816.19)100 0 O00 |33133 2.23 OX S uo w Hhe stem The mode