Dynamics Problem with a Driving Force, 2 Wheels, a Spring and a Damper

In summary, dynamics is the study of the forces that cause changes in the motion of objects. A driving force is an external force that can push or pull an object in a specific direction. A spring, which is an elastic material, can affect the dynamics of a system by providing resistance or support to the movement of an object. A damper, on the other hand, is used to control the speed and stability of a moving object by dissipating kinetic energy. The two wheels in a dynamics problem can represent the movement of a system and contribute to its overall energy and momentum. Finally, the main difference between statics and dynamics is that statics deals with stationary objects while dynamics deals with moving objects.
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rakan
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Homework Statement
The input to the system shown below is the force F_i(t). The two identical wheels with
radius r roll without slip. Each wheel has mass M_w and rotational inertia 𝐽 = 𝑀_𝑀 π‘Ÿ^2/2; the connector
bars each have mass M_b. The spring is linear with stiffness K and the viscous damper is linear with coefficient b. The bearings at the center of the wheels are frictionless.

4.1 Draw the free body diagram for getting the component equations for the system shown below.

4.2 Write the component equations.

4.3 Verify that the component equations combine and simplify to the following simultaneous
equations:
(1.5*M_w + M_𝑏)π’—Μˆ + 𝒃𝒗̇ + π’Œπ’— = 𝒃𝒖̇ + π’Œπ’–
(1.5*M_w + M_𝑏)π’–Μˆ + 𝒃𝒖̇ + π’Œπ’– = 𝒃𝒗̇ + π’Œπ’— + 𝑭_π’Š

4.4 Explain why four state variables are required to simulate this system using ode45; what are
these state variables and what are the equations for their derivatives?
𝒙̇_𝟏 =? 𝒙̇_𝟐 =? 𝒙̇_πŸ‘ =? 𝒙̇_πŸ’ =?
Relevant Equations
(1.5*M_w + M_𝑏)π’—Μˆ + 𝒃𝒗̇ + π’Œπ’— = 𝒃𝒖̇ + π’Œπ’–
(1.5*M_w + M_𝑏)π’–Μˆ + 𝒃𝒖̇ + π’Œπ’– = 𝒃𝒗̇ + π’Œπ’— + 𝑭_π’Š
1662349775342.png
 
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What are your thoughts so far?
 

Related to Dynamics Problem with a Driving Force, 2 Wheels, a Spring and a Damper

1. What is a driving force in a dynamics problem?

A driving force is any external force that is applied to a system to cause it to move or change its motion. It can be a physical force, such as pushing or pulling, or a non-physical force, such as an electromagnetic force.

2. How do the 2 wheels in a dynamics problem affect the system?

The 2 wheels in a dynamics problem act as points of contact between the system and the ground. They determine the direction and magnitude of the system's motion and can also provide resistance or support to the system's movement.

3. What is the role of a spring in a dynamics problem?

A spring is a component that stores and releases energy in a system. In a dynamics problem, a spring is often used to model the elasticity and stiffness of a material, and it can affect the system's motion by providing a restoring force.

4. How does a damper impact a dynamics problem?

A damper is a device that dissipates energy in a system, typically in the form of heat. In a dynamics problem, a damper can reduce the amplitude of oscillations and dampen the system's motion, leading to a more stable and controlled behavior.

5. What are some real-world applications of a dynamics problem with a driving force, 2 wheels, a spring, and a damper?

This type of dynamics problem can be applied to various systems, such as a car suspension system, a door with a spring hinge, or a mechanical arm with a damper. It can also be used to study the behavior of oscillating systems, like a swing or a pendulum.

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