Simple Harmonic Motion: Maximum Velocity and Acceleration Calculation

AI Thread Summary
The discussion revolves around calculating the maximum velocity and acceleration of a body in simple harmonic motion with a total movement of 200mm and a frequency of 6Hz. Participants clarify the equations for velocity and acceleration, emphasizing the relationship between angular frequency (ω) and frequency, noting that ω equals 2π times the frequency. The maximum velocity (vmax) is derived from the formula vmax = ωA, where A is the amplitude. There is confusion regarding the maximum values in trigonometric functions, but the focus remains on applying these principles to find the required calculations. The conversation highlights the importance of understanding the underlying equations and relationships in simple harmonic motion.
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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