2. Derive the equations of motion [Due date: 26/2/2024] [40%] Once the proposal is accepted by the instructor (or improved/corrected), each group should work independently to derive the equations of motion and all required supporting equations and constraints (if applicable). For this you need to do/provide the following: • Establish a reference point on the path to measure the particle position from. This is the s = 0 point. You may need to use two coordinate systems to relate the path equation to the position along the curve. Assume an arbitrary position in the positive sense for your particle along the path. • Prepare the FBD and KD at that arbitrary position. • Write the equations of motion. • Write any required auxiliary constraint equations you may need to check for if the particle stops momentarily or the speed changes directions. • Use the attached template for your report (must use it). 3. Matlab Simulation [Due date: 25/3/2024] [40%] Each group should write a Matlab script to simulate the particle motion for a number of possible motion scenarios (5 cases). Verify or correct your equations as per the instructor's feedback in part 2. Write the required Matlab script (code). • Simulate the system response for a given initial condition (plot the position and velocity of the particle versus time) • The simulation should be done for 5 different cases (various combinations of friction coefficient, μk, and spring stiffness, k, see the report format) Explain the results as per your expectation of the real system response./n UAEU College of Engineering جامعة الإمارات العربية المتحدة United Arab Emirates University Department of Mechanical Engineering MECH 310: Dynamics 2nd Semester 2023/2024 Term project Part 1: Proposal Submitted by Date: 13/2/2024 Max. Group Related Related Section grade grade CLO PLO Proposal description Sketch of the particle and constraints 5 5 List of the acting forces (must be 4 or more) and any required curve/constraint equation 10 Total 20 Student 1 grade Verification part: Q&A for each student to Student 2 grade verify contribution Student 3 grade 1 Project proposal 1.1 System description with sketch (2D or 3D) - - It's a 2-D problem. A slingshot is for throwing or launching a solid projectile. The slingshot is made of a frame, two flexible ropes, and a solid projectile. The frame for installing the elastic ropes, and the elastic ropes are often a rubber band, is like a pre-take-off. When it is stretched it stores a lot of energy to push the solid material we stretch the particle then bounces on a surface. As for the projectile, it is the body that we launched, after throwing the particle it bounces on a surface. FBD Elassroomclipart.com y FF mg E 1.2 List of the acting forces - Tension - Weight Friction - Air resistance 4 7x 1.3 Surface or path equation if needed particle Bounces on 9 Surface es AN AF B mg 2 T es AF surface AN mg

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