The double pendulum is shown in Figure 2.1. Parameters for this double pendulum are 4 =...

 

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The double pendulum is shown in Figure 2.1. Parameters for this double pendulum are 4₁ = 0.2 m, l₂ = 0.4 m, m₁ = 0.02 kg, m₂ = 0.04 kg. 4 3/₂ m₂ Figure 2.1: Double pendulum Requirements for Question 2: (a) Derive the differential equations of motion for the double pendulum using the coordinates ₁ and ₂ and assume small angles. (b) Derive the differential equations of motion for the double pendulum coordinates X₁ and x₂ and assuming small amplitudes. (8 marks) using the (4 marks) (c) Find the response of the free vibration of the system with 8₁ (0) = -0.57 rad, ₁ (0) = 0 rad/s, 0₂ (0) = 1.57 rad, 0₂ (0) = 0 rad/s x₁ (0) = -0.1 m, x₁ (0) = 0 m/s, x₂ (0) = 0.2 m, x₂ (0) = 0 m/s Plot the response figures and give some comments. (8 marks) 8₁ m₁ ½₂ The double pendulum is shown in Figure 2.1. Parameters for this double pendulum are 4₁ = 0.2 m, l₂ = 0.4 m, m₁ = 0.02 kg, m₂ = 0.04 kg. 4 3/₂ m₂ Figure 2.1: Double pendulum Requirements for Question 2: (a) Derive the differential equations of motion for the double pendulum using the coordinates ₁ and ₂ and assume small angles. (b) Derive the differential equations of motion for the double pendulum coordinates X₁ and x₂ and assuming small amplitudes. (8 marks) using the (4 marks) (c) Find the response of the free vibration of the system with 8₁ (0) = -0.57 rad, ₁ (0) = 0 rad/s, 0₂ (0) = 1.57 rad, 0₂ (0) = 0 rad/s x₁ (0) = -0.1 m, x₁ (0) = 0 m/s, x₂ (0) = 0.2 m, x₂ (0) = 0 m/s Plot the response figures and give some comments. (8 marks) 8₁ m₁ ½₂

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Let us take the free body diagram of m2 Mass Mi Av so... View the full answer