2. Consider the system given in Figure 2. (a) Write down the Lagrangian for this system. [4 marks] (b) Applying Lagrange

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2 Consider The System Given In Figure 2 A Write Down The Lagrangian For This System 4 Marks B Applying Lagrange 1 (45.2 KiB) Viewed 20 times

2. Consider the system given in Figure 2. (a) Write down the Lagrangian for this system. [4 marks] (b) Applying Lagrange's equations, write down the equations of motion. [4 marks] (c) Express the equations in matrix form MX + KX = 0, where M is the mass matrix, K is the stiffness matrix and X is the position vector. [2 marks] (d) Assume k₁ = 2kg, k₂= 5kg, m₁ = 1kg, m₂ = 2kg and m3 = 3kg. Also assum a mode shape: X = 3 XX, determine a natural frequency of [5 marks] = XTMX Using Rayleigh's method, R(X) = the system. (e) State two merits of the Rayleigh method. [2 marks] (f) Explain briefly how the system can be excited such that it moves according to a mode. [2 marks] (g) If a second natural frequency is zero, comment on the corresponding mode i.e. how would the system move? [1 mark] m₁ m₂ wm a) I -X₁ 1 Figure 2: This Figure refers to Question 2. Xz 3