Question

Input:trolley acceleration TrolleyOutput: trolley displacement and payload swing angle Assumptions trolley is unaffected by motion of the payload due to the large mechanical impedance in the drive system. damping from air is approximately zer. small oscillations around the equilibrium angles yields: 0. Payload Fig 1. model of a planar crane. Sin0)- Cos(0) Question: Modeling: nonlinear differential equations Linearized equation: linear differential equations, transfer function, and state space equation. Dynamics Analyses Natural frequency versus cable length, Fig. 2 Vibration amplitude versus driving motions and cable length, Figs. 3,4

Answer 1

Position of payload mi velocity- m2 Payload K-E OF system. = k. E oF trolley t k-E of Payload ะ 2miz? t 흘ma2 {2e2 t ee2-2Lx.cose e} PE of system Lagrangian oF system 2 Using lagrangian approach For% at?-와 :0 Using singn9, cos9- Fore dt

Non-Linear Differential Equations describins the motion are