Fig. Q4 shows a spring-mass system in which m and m are the masses and k...

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Fig. Q4 shows a spring-mass system in which m₁ and m₂ are the masses and k₁ & k₂ are the stiffnesses of the springs. Determine the equations of motion using Newton's laws of motion. Verify your result by the Lagrange method. If m₁ = m, m₂ = 4m, k₁= k and k₂ = 2k, show that the frequency equation can be expressed as k k @ -1.75 +0.5 = 0, where w is the natural frequency of vibration. m - m Also determine the natural frequencies in terms of k and m. mi k₁ ]mün[ m2 Fig. Q4 k₂ mür Fig. Q4 shows a spring-mass system in which m₁ and m₂ are the masses and k₁ & k₂ are the stiffnesses of the springs. Determine the equations of motion using Newton's laws of motion. Verify your result by the Lagrange method. If m₁ = m, m₂ = 4m, k₁= k and k₂ = 2k, show that the frequency equation can be expressed as k k @ -1.75 +0.5 = 0, where w is the natural frequency of vibration. m - m Also determine the natural frequencies in terms of k and m. mi k₁ ]mün[ m2 Fig. Q4 k₂ mür

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