How Do You Calculate Dynamics of a Mass Spring System?

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Homework Help Overview

The discussion revolves around calculating various aspects of a mass-spring system, specifically focusing on total mechanical energy, maximum speed, maximum acceleration, and speed at a given displacement. The subject area is dynamics within the context of oscillatory motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of the mechanical energy equation, questioning how to apply it correctly with given values. There is a discussion on the significance of amplitude and displacement in the context of energy calculations.

Discussion Status

Some participants have provided guidance on using the mechanical energy formula and emphasized the importance of unit conversion. Multiple interpretations of how to approach the calculations are being explored, particularly regarding the relationship between displacement and velocity.

Contextual Notes

There is a mention of the need to convert units from centimeters to meters for consistency in calculations. The original poster's attempt at a solution raises questions about the accuracy of their calculations and the application of the equations provided.

deliliah
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Homework Statement


a mass spring system vibrates with an amplitude of 4.5 cm. if the spring has a constant od 250 n/m and the mass is 400 kg determine the
a) total mechanical energy
b) the maximum speed of the mass
c) the maximum acceleration
d) the speed of the mass when the displacement is 2.0 cm


Homework Equations



e= 1/2mv^2 + 1/2 kx^2
e= 1/2 ka^2 = 1/2 mv^2(max)
e=1/2 mv^2 + 1/2 kx^2
e= 1/2 mv^2 + mgh

The Attempt at a Solution


1/2 (400)(0)^2 + 1/2 (250)(4.5)^2= 2531.25?
 
Last edited:
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If the amplitude is 4.5 cm then when x=4.5 cm, then v=0. Can you start with that?
 
so would i just use the 1/2 mv^2 + 1/2 kx^2 for the total mechanical energy? and just plug in 4.5 for x and 0 for v?
 
deliliah said:
1/2 (400)(0)^2 + 1/2 (250)(4.5)^2= 2531.25?
so would i just use the 1/2 mv^2 + 1/2 kx^2 for the total mechanical energy? and just plug in 4.5 for x and 0 for v?
Yes, that will work. But make sure you convert 4.5 cm to meters, if you want your final answer in units of Joules.
 

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