A thin, uniform rod of length 2L and mass M is suspended from a massless string of length / tied to a nail. As shown in

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A Thin Uniform Rod Of Length 2l And Mass M Is Suspended From A Massless String Of Length Tied To A Nail As Shown In 1 (55.45 KiB) Viewed 32 times

A thin, uniform rod of length 2L and mass M is suspended from a massless string of length / tied to a nail. As shown in Figure 1, a horizontal force F is applied to the rod's free end. X 0₁ 2L F F (a) (b) Figure 1 1. Take the inertia of the rod to be M³ and show that the Lagrange's equations of motion are as follows: MIÖ₁ + M LÖ₂cos (01-02) + MLO sin(01-02) + Mg sino₁ = F cos0₁ 4 M LÖ₂ + Mlö¹cos(0₁ - 02) – MIO² sin(0₁ - 02) + Mg sin02 = 2F cos02 2. Rewrite the equations assuming that all angles are small. Show your steps. Mg