As shown in the figure on the right, a slider with mass m1 is connected to...

  

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As shown in the figure on the right, a slider with mass m1 is connected to the foundation with two springs with stiffnesses k1 and k2; there is a simple pendulum with mass m2 and pendulum length 1 on the slider. Assume m1= 4m, m2=m, k1=k2=k, the foundation undergoes simple harmonic motion in the horizontal direction X = a sin wt, where w = √√k/m 1) Apply the Lagrange equation to derive the differential equation of the system for micro-vibration: 2) Solve for the natural frequency and mode shape of the system: 3) Solve the steady-state response of the system under basic excitation and determine the maximum swing angle of the simple pendulum /theta max e 772 As shown in the figure on the right, a slider with mass m1 is connected to the foundation with two springs with stiffnesses k1 and k2; there is a simple pendulum with mass m2 and pendulum length 1 on the slider. Assume m1= 4m, m2=m, k1=k2=k, the foundation undergoes simple harmonic motion in the horizontal direction X = a sin wt, where w = √√k/m 1) Apply the Lagrange equation to derive the differential equation of the system for micro-vibration: 2) Solve for the natural frequency and mode shape of the system: 3) Solve the steady-state response of the system under basic excitation and determine the maximum swing angle of the simple pendulum /theta max e 772

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Here are the steps to solve this problem using Lagrangian mechanics 1 Derivation of the differential ... View the full answer