Question

just simple answers and equations for 3 and 4th problems to solve in Mathcad

Vibrations and Acustics Name, SurnameStudent ID Computer NR Nr. -4 System with moving base, Differential equation. Degree of Freedom. 3. 1. 2. Establish motion differential equation and obtain displacement and velocity graphs in time for all objects. Use Force balance method! Gravity force, friction force and air resistance is active. Air temperature is 20C9. Cube edge size a-0.05m. Motion possible only in x direction. Given: m-lkg, KI-50N/m, K2-1.5K1, c-o8Nsm: "-0.3. Force F(t) is acting on system: 3T Fetn K2 4. Establish motion differential equation and obtain displacement and velocity graphs in time for all objects. lise Lagrangian's method Air resistance is neglected. Given: ml-0.5kg: m2-lkg: L-1.1m; R-0.05m; K1-80N/ml K2-1.2K1; C-0.8 Ns/m. Initial displacement m I(a-3) KI L/2 Exam CourseWAttendance Final

Answer 1

Free-Body Diagram る Fp Resistance due to air friction F(t) mg uN Applying Neroton's Lai =mx. In x-direction : Σ Jn Y-direction Fy my since no motion alony yy () becomes 0,3 cossnt) tol sin (29 +0.8 χ t 125χ t 2.943 t FD 4 K2 m2 R mi Kinetic Enercy of system 2 12* 12 2 2 L2 2 2 12

Potentiol Energy of system = 14.526 + 40 [0.302582十0.002507-0.055662] = 14 gaga 0167t 26:62 θ를-229,92 Energy Dissipated Lagrangian(L)K E- PE = 3-125x10-4G2 +0025292-016f-2662d-22 ON, Using Lagrangian approath For θ」 dtae a6, 261 dt 6.25x10-4 e, + 0.291-2.282 = o For 2 00504 θ2 + 53.24 θ2-229, +0.24289 o .: EoM in matrix form Ou 021"L-22 53.2小θ2 0.242|1621-16 00504 (62