Solve Mass of Glider with Harmonic Motion Help

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Homework Help Overview

The problem involves a glider oscillating on a frictionless air track attached to an ideal spring, with the goal of determining the mass of the glider based on its acceleration over time and the spring's force constant.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of the period of oscillation and its implications for determining the mass. There are attempts to verify the period based on the acceleration graph and questions about the correctness of their calculations.

Discussion Status

Participants are actively exploring different values for the period and questioning their calculations. Some have identified a potential period of 0.10 seconds, but there is uncertainty regarding the accuracy of their mass calculations. No consensus has been reached on the correct approach or values.

Contextual Notes

There is a mention of confusion regarding the period of the sine wave and its relationship to the calculations for mass. Participants are also grappling with the implications of their findings on the overall problem.

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Homework Statement


On a frictionless, horizontal air track, a glider oscillates at the end of an ideal spring of force constant 2.20 N/cm . The graph in the figure shows the acceleration of the glider as a function of time.
Find the mass of the glider.

YF-13-31.jpg




Homework Equations


T= 2pi\sqrt{m/C}



The Attempt at a Solution


2.2 N/cm = 220 N/m
C=220

.4 = 2pi\sqrt{m/220}
m = 1389

I know I'm doing something wrong but what?
 
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How much is the period of the sine wave ?
 
would it be .2s? when it passes back through O and to where it started?
 
I tried .2 and .3. are any of these the right time for period? If so then my problem lies elsewhere. any insight? thanks
 
okay i see now. .10 is the time for a period.

so .10 = 2pi \sqrt{m/220}

multiply both sides by \sqrt{220}

1.48 = 2pi\sqrt{m}

divide both sides by 2pi

2.43 = \sqrt{m}

square both sides

m = 5.43 which is still the wrong answer.

is my math wrong? what exactly am i doing wrong?
 

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