Is my forced spring-mass system correctly modeled with these equations?

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In summary, the conversation is about a spring-mass system that is initially in equilibrium and is then set into motion by a force applied and released at t0. The system will continue to move around the equilibrium position until the restoring force from the spring balances the gravitational force. The discussion also includes equations and the difficulty of accounting for the gravitational force and the forcing term in the differential equation.
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Shackleford
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After the spring-mass is in equilibrium, a force is applied then released at t0 and the spring-mass system is set into motion. For a certain period of time the spring-mass will move around the x0 equilibrium position until the restoring from the spring has balanced the gravitational force.

Are my two equations correct? I guess I'm having trouble accounting for the gravitational force and the forcing term in the DE. Otherwise, it would be a simple homogeneous equation with x = A cos(w0t).

http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-21193429.jpg?t=1285115763

http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-21193118.jpg?t=1285115676
 
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Anyone? Eh?
 

Related to Is my forced spring-mass system correctly modeled with these equations?

1. What is a forced spring-mass system?

A forced spring-mass system is a physical system that consists of a mass attached to a spring and subjected to an external force. The external force causes the mass to oscillate around an equilibrium position, and the spring provides the restoring force that brings the mass back to its equilibrium position.

2. How does a forced spring-mass system behave?

The behavior of a forced spring-mass system depends on the characteristics of the system, such as the mass, spring constant, and the properties of the external force. Generally, the system will oscillate with a specific frequency, amplitude, and phase, which can be calculated using mathematical equations.

3. What is the difference between a forced and unforced spring-mass system?

An unforced spring-mass system is one in which there is no external force acting on the mass, and it is only subjected to the restoring force of the spring. In contrast, a forced spring-mass system has an additional external force acting on the mass, causing it to oscillate with a specific frequency and amplitude.

4. How is a forced spring-mass system used in real-world applications?

Forced spring-mass systems have many practical applications, such as in mechanical engineering, where they are used to design and analyze systems such as car suspensions, shock absorbers, and vibration isolators. They are also commonly used in seismology and earthquake engineering to model the behavior of buildings and structures during seismic events.

5. What factors can affect the behavior of a forced spring-mass system?

The behavior of a forced spring-mass system can be affected by various factors, including the mass of the object, the stiffness of the spring, and the characteristics of the external force. Other factors that can influence the system's behavior include friction, damping, and the initial conditions of the system, such as the amplitude and phase of the oscillations.

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