Determine the motion expressions for each of the systems shown below by using the Euler-Lagrange equation. not skiping steps please explain i do not understand yet Pendulum of length (l) and mass (m) whose support rotates in a circle of radius (a)  in a vertical plane, with constant angular velocity ω as shown in the figure

P.4) You are tossing the baton up into the air while it is turning, resulting in a motion that is translating as well as rotating. The instance when the baton was tossed into the air is illustrated in a figure below. The baton is modeled as two point masses m attached at the end of a massless rod of length 2r. The center of the rod is thrown directly upward at a speed vo. The rod rotates at an angular speed of è. Derive the expression for the kinetie energy for the baton's motion (translation and rotation at this instance) using the given variables. /B

Please help answer the question shown in the photo. The topic is System Dynamics, Mechanical Engineering. I do not know how to solve it. Please explain all steps clearly and how you solved it. Any help will be much appreciated. Thank you!

Problem 4.8 for reference, i only need bottom half

A solid bar of mass m and length L stands vertically on a frictionless table and is then released to fall down. The moment of inertia about the center of mass is Ic = mL²/12. At the moment when the top end B just reaches the ground (0-0), (a) what are the angular velocity and angular acceleration? (b) what is the center-of-mass acceleration? (c) what is the normal force of the ground to end D? Hint: It may be helpful to find out the instant rotation axis. В m. L D

I need a clear and fast answer within 20 minutes. Thank you

Derive the equations of motion using Lagrange's equations. (I, =mr? ) THE MOTION IS ON THE HORIZONTAL PLANE (NO GRAVITY) Trailer, mass M Cylinder, k1 mass m k2

Problem #2) The thin plate ABCD has mass 10kg and is held stationary in the position shown (p= 30°) by a wire BH and the two massless parallel links AF and DE. At t = 0sec, the wire is cut and the plate is released from rest; it immediately moves in a pure translation motion due to the system's geometric constraint by the links. Find the forces in each link immediately after the wire is cut. All dimensions are in millimeters. 150 A D -500 H B IC T 200

A block of mass 40 kg slides to the right due to the application of the force T. Neglect the mass of the pulleys. 30° 40 kg T = 100 N Hy = 0.50 Hp = 0.40 A Figure Q6 (a) Set up the global reference axes system and draw the free body, kinematic and kinetic diagrams of the block.

Major keep in mind the steps give below