Help finding equation of motion

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Homework Help Overview

The problem involves a mass-spring-damper system where a 1/4 kg mass is attached to a spring with a stiffness of 4 N/m and a damping constant of 1 N-sec/m. The mass is initially displaced 1/2 meter upward and given an initial velocity of 1 m/sec upward. The goal is to find the equation of motion and the maximum displacement of the mass.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the spring equation and expresses uncertainty about how to proceed. Some participants inquire about the familiarity with differential equations and the specific equation of motion for a damped oscillator. Others provide the general form of the equation of motion and ask if the original poster knows how to solve for displacement.

Discussion Status

The discussion is ongoing, with participants exploring the formulation of the equation of motion and questioning the original poster's understanding of the necessary concepts. Guidance has been offered regarding the general technique for solving the equation, but no consensus or resolution has been reached.

Contextual Notes

There is an indication that the original poster may not be familiar with differential equations, which could impact their ability to proceed with the problem. Additionally, the discussion includes the need to incorporate initial conditions into the solution process.

bengaltiger14
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Homework Statement




A 1/4kg mass is attached to spring with stiffness of 4N/m. The damping constant for the system is 1 N-sec/m. If the mass is displaced 1/2 meter up and given an initial velocity of 1 m/sec upward, find the equation of motion. What is the maximum displacement that the mass will attain??

I don't know how to get started with this. I know the spring equation Fs=-kx. So, Fs would just equal 1 N Kg/m. I just don't know what to do. Any help would be appreciated.
 
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Since you posted this in Introductory Physics I assume you aren't familiar with differential equations. In that case you would have to have been taught the equation of motion for a damped oscillator. Is that the case? Are there any equations that your teacher has presented on this?
 
I have the equation: (m)y(doubleprime(t)) + gamma(y prime(t)) + ky(t)=0

m = .25kg/(9.81 m/second^2)
gamma = 1N-s/m k=4N/m

so, the equation of motion is:

0.025y(doubleprime) + y(prime) + 4y=0
 
And for an equation of that type, do you know how to solve for y(t)? If you have the general technique, you should be able to enter in your boundary conditions (initial speed, initial displacement) during intermediate steps to get to an expression for displacement.
 

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