Simple Harmonic Motion: Maximum Velocity and Acceleration Calculation

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Homework Help Overview

The discussion revolves around a problem related to simple harmonic motion, specifically focusing on calculating the maximum velocity and maximum acceleration of a body oscillating with a given frequency and amplitude.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the equations for velocity and acceleration in simple harmonic motion, questioning the conditions under which maximum values occur. There is an exploration of the relationship between angular frequency and frequency, as well as the maximum values of trigonometric functions involved.

Discussion Status

Some participants have shared equations and are attempting to clarify concepts related to maximum values in oscillatory motion. There is ongoing exploration of the relationships between different parameters, but no consensus has been reached yet.

Contextual Notes

Participants have noted a lack of class notes and are working from memory and external resources, which may affect their understanding of the problem. There is also a mention of uncertainty regarding the maximum values of trigonometric functions in the context of the problem.

daveiejbeer
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The total movement of a body oscillating with simple harmonic motion is 200mm. If the frequency of oscillation is 6Hz, determine the maximum velocity and maximum acceleration of the body.

I missed the class when this was done so I haven't got the notes. I am not sure if this is right but I found these equations

v = w Acos wt
a = -w2 Asin wt = -w2y

Anyone point me in the right direction please?
 
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daveiejbeer said:
The total movement of a body oscillating with simple harmonic motion is 200mm. If the frequency of oscillation is 6Hz, determine the maximum velocity and maximum acceleration of the body.

I missed the class when this was done so I haven't got the notes. I am not sure if this is right but I found these equations

v = w Acos wt
a = -w2 Asin wt = -w2y

Anyone point me in the right direction please?

If you know v=ωA*cosωt

vmax will occur when cosωt is maximum, so cosωt is what number?
 
I found this info http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm so I am reading this.
 
Last edited by a moderator:
Im still none the wiser!
 
daveiejbeer said:
I found this info http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm so I am reading this.

daveiejbeer said:
Im still none the wiser!

Well let's start simple. For the graph of y=sinx, what is the maximum value of y? (the graph oscillated between?)


what is the relationship between ω and the frequency?
 
Last edited by a moderator:
Is the max value of y 1? Going back to trig and waveforms.
Isn't ω 2∏ times the frequency?
 
daveiejbeer said:
Is the max value of y 1? Going back to trig and waveforms.
Isn't ω 2∏ times the frequency?

Right, so wouldn't

vmax=ωA ?
 

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