Dampened harmonic motion question

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Homework Help Overview

The problem involves dampened harmonic motion related to an automobile's suspension system. The original poster seeks to determine the spring constant and damping constant based on given parameters, including mass and oscillation characteristics.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply Newton's second law to find the spring constant and expresses uncertainty about the damping constant and the time variable in the equations. Some participants suggest developing the damped harmonic oscillator equation to clarify the relationship between oscillation period and damping.

Discussion Status

The discussion includes attempts to solve for the spring constant and damping constant, with some participants providing insights about the period of damped oscillations. There is a mix of approaches being explored, and while some guidance has been offered, there is no explicit consensus on the methods being used.

Contextual Notes

Participants are working under the constraints of the problem statement, including specific mass values and the behavior of the suspension system. The original poster's uncertainty about certain variables and the need for clarification on oscillation periods are noted.

sigmavirus
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Homework Statement


Automobile of mass m=2000kg has a suspension that sags 10 cm when the entire auto is placed on it. The amp. of oscillation decreases 50% with every complete oscillation. Solve for (a) spring constant k and (b)the damping constant b for one wheel (assuming each wheel supports 500 kg).


Homework Equations


Fspring=-ky
Fdrag=-bv
y(t)=ymaxe-bt/2m


The Attempt at a Solution


I think i should use [tex]\Sigma[/tex]F=ma for the initial force, which would be gravity ant the spring. so mg=-ky then solve for k. i am not sure how correct this is, though. then for part b, i don't know what to do about t in the equation and i was considering using a variable (so t/2 for the 2nd oscillation)
 
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You need to develop the damped harmonic oscillator equation of motion. Otherwise you don't know how long one complete oscillation lasts.

Though if you haven't studied this, I can tell you that the period of a damped oscillation, is very VERY close to that of the undamped oscillation. (I'm talking differences in the third or fourth digit here)

[tex]\omega_{damped}\approx \omega_0=\sqrt\frac{k}{m}[/tex]
 
i solved it using a period of 2[tex]\pi[/tex]. thanks for the help!
 
sigmavirus said:
i solved it using a period of 2[tex]\pi[/tex]. thanks for the help!

Are you sure? Since that doesn't have the right units.

Did you mean [tex]\frac{2\pi}{\omega}[/tex] ? If so, then you're correct. :)
 

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