Find position after t for simple harmonic motion

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Homework Help Overview

The problem involves a block undergoing simple harmonic motion (SHM) on a frictionless air track, with specific parameters including mass, equilibrium position, and period. The original poster seeks to determine the position of the mass after a certain time following its release from a displaced position.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of equations related to SHM, including those for position, amplitude, and angular frequency. Questions arise regarding the calculation of amplitude and the correct application of the position formula. There is also a mention of needing a phase angle for accurate position determination.

Discussion Status

The discussion includes attempts to apply various formulas to find the position of the mass and to understand the implications of the initial conditions. Some participants have provided guidance on the necessity of including a phase angle in the position equation, while others express uncertainty about their calculations.

Contextual Notes

Participants note the importance of initial conditions and the potential impact of incorrect assumptions on the calculations. There is a mention of a second part of the problem regarding maximum acceleration, indicating that the discussion may extend beyond the initial query.

smillphysics
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A 28.0 kg block at rest on a horizontal frictionless air track is connected to the wall via a spring. The equilibrium position of the mass is defined to be at x=0. Somebody pushes the mass to the position x= 0.350 m, then let's go. The mass undergoes simple harmonic motion with a period of 4.70 s. What is the position of the mass 3.854 s after the mass is released?

T=2pi*sqrt m/k
KE1+PE1=KE2+PE2 from this you get mv^2=KA^2
x=Asin *omega*t
omega=2pi*frequency
frequency =1/T

I used the first equation get k=3.92
then I use that k in the second equation, but I don't know how to get v to then get A. Any help? Would I then take that A and plug it into the third equation to get my X?
 
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In the given problem the amplitude A is given. ( 0.35 m). Find x.
 
So I plugged in A (.35m) into the equation,
x=.35sin(1.34*3.854) and got x=.032 which is still incorrect? Any help on where I am going wrong?
The second part of this problem calls for the maximum acceleration- would I use the equation a=omega^2cos omega *t? I don't think that I will get this problem correct if I got the last one incorrect.
 
Your formula for posistion does not work at t=0! You need a phase angle in it, or use cosine instead of sine.
 
I figured this problem out. Thank you!
 

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