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4. Consider a 3-DOF system that is subjected to a harmonic force as shown below. The force has the form f(t) = Fcos(wt) where F = 10 N, and the system parameters are m₁ = 3 kg, m2 = 15 kg, m3 = 7 kg, k₁ = 100 N/m, k₂ = 200 N/m, k3= 150 N/m. f(t) k₂ k₂ k₁ m m₁ m ние тз x3 x x2 a) Write the equations of motion for the system in matrix form. b) Find the natural frequencies and modes of the system. c) At what forcing frequencies w will the mass m2 be stationary? d) If the mass m2 is increased to 20 kg, how does the answer to c) change? e) Now with m2 = 20 kg, what is the magnitude of the displacement response of mi if the forcing frequency is equal to the frequencies you found in d)? f) Briefly (a few sentences) explain the results of parts c) through e). m₂ тг