TBR Phys. Periodic motion

[bdc142]

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I'm a bit confused about Figure 5-3 which shows two graphs of damped harmonic oscillation - ampltidue vs. time and energy (KE and PE) vs. time.

It shows that when it is at -amp, there is a min in PE and a max of KE. Isn't this wrong?

Thanks!

 

[411309]

At at lower amplitude PE is at a minimum and KE is at a max. Think of a pendelum. At it's highest point (amplitude) it has the most PE because of the most height- mgh. As it begins to descend and lose amplitude it turns into KE and KE maximizes at the lowest point, upon its ascension it loses KE as it becomes PE again. So you have mgh=1/2mv^2 . In dampened harmonic motion you're losing energy upon each oscillation so the KE values and PE values are slowly declining.

 

[bdc142]

Hrm...but what if it was a damped harmonic oscillation of a block attached to a spring on a surface? -amp and +amp would have max PE and min KE, right?

 

[411309]

yes, because its at the maximum distance from equilibrium 1/2kx^2 the higuher the x the higher the potential energy.

 

[bdc142]

Ah ok, thanks! Just wish TBR would've specified that the graphs were for a pendulum and not marketed as a general thing...

 

[pfaction]

Wait, did I misunderstand?

It shows that when it is at -amp, there is a min in PE and a max of KE. Isn't this wrong?

It should be wrong, because at Amp and -Amp the PE is max, KE is min?

PE is deltaX squared, so whether it's amp or -amp, the PE will be max at the |amp|, indicating KE is min.

 

[411309]

This is kind of confusing the picture that TBR has. Im assuming by negative amp they mean amp is decreasing and its reverting back to equilibirum.

 

[bdc142]

This is kind of confusing the picture that TBR has. Im assuming by negative amp they mean amp is decreasing and its reverting back to equilibirum.

Yep. Like this: http://www.google.com/imgres?imgurl...=1t:429,r:0,s:0&tx=115&ty=64&biw=1708&bih=726

So using that image, TBR is saying that when it's at "-A", the PE is minimum, and kinetic energy is max.

 

[411309]

Yep. Like this: http://www.google.com/imgres?imgurl...=1t:429,r:0,s:0&tx=115&ty=64&biw=1708&bih=726

So using that image, TBR is saying that when it's at "-A", the PE is minimum, and kinetic energy is max.

I like that picture better.

 

[bdc142]

Looking at the figure again...the amplitude vs. time graph has amplitude in the 'x' direction, therefore eliminating the possibility that it is a describing a pendulum. I guess TBR just screwed this up 🙁