Question

Can someone please help me with this problem? *****The correct solution is listed below, so please come to that same solution.***** If you can offer a little explanation in trickier steps, that would be great, but I understand if not.

Problem 2.33 In the pulley system shown below, assume that the cable is massless and inextensible. Assume that only mass of pulley 2 is negligible. Derive the system’s equations of motion in terms of the displacement Xi. (note: include dynamics of pulley 1 in the equation) Answer: Rest (mı + ) ën + n = f k 2 Rest FIGURE P2.33

Answer 1

X_1 = theta times R theta = x_1/R total energy of system dE = 1/2 m_perpendicular x^2_perpendicular + 1/2 r_p theta^2_perpendicular + 1/2 kx^2_2 - fx_perpendicular = 1/2 m_perpendicular x^2_1 + 1/2 I_P x^2_1/R^2 + 1/2 k (x_1/2)^2 dE/dt = 0 => d/dt [1/2 (m_perpendicular + I_P/R^2) x^2_1 + 1/2 (k/4) x^2_1 - fx_perpendicular]= 0 => 1/2 (m_perpendicular + I_P/R^2 2x_perpendicular x-perpendicular + 1/2 (k/4) 2x_perpendicular x_perpendicular - fx_perpendicular = 0 => (m_1 + I_P/R^2) x_perpendicualr + k/4 x_perpendicular =