Question

1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's equations. Find the natural frequencies and mode shapes of the dynamical system for k 1 N/m, k-2 N/m, k I N/m, and mi 2 kg, m l kg, m -2 kg. scale the eigenvectors matrix Ф in order to achieve a mass normalized eigenvectors matrix Φ such that: F40 Fan Fig. 1

Answer 1

r3 amd hace displacement vequise thaee eiction of motion Toịal kinetic ene09 CJne to mass) 2 Totat potential eme0Zy(Due to SPring 2 2 z)Use lang20.rge's eate tior Foơ mASS-γη ĩ 2 ax Pat the vale in the eqic tion , aU an ar 3 Prst the Vae im the eqtom

3) Use lemgaamge's equation foơ mass 3 mctaja foam of eauatiom F1c) 2Ct 3Ct) 3 O -22 The eigenvobern Sohition of the Sstem So. Solu) Solve for eigen vlues CX) 2. 3ーズ let

ase Scientific calculator fo AYdin three v9rue of λ S. 182 2 2 -G.188 2 1327-45S φ12-一2.534 -2-S32 2.458 1.627