Solve Unknown Spring Equation from Foxtrot Comic Strip

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BluberryPi
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Hey, I am a new member, and I have a question. One of my favorite comic strip is foxtrot because it has so much physics:smile:! When I read this particular strip, however (7/30/2000- find it on Foxtrot GoComics) I was puzzled by the equations. Fortunately, 4 of them were printed in the Gocomics comments. Unfortunately, one was not really defined! Can someone please find this physics equation, explain it to me, and cite the source in which you got it from ? Thank You! The formula is in panel 4. By the way, the boy's name is Jason.http://api.ning.com/files/RlUkQ9Zps*RjiCqr6VvmdeH7x2Srx0GsPXjfQgGYD5GaS1MCjIQ6c7dIk0g4pZ7ZR5NDYsPIC6sq60J6WzrAiUBXxDattOV-/foxtrotplayground.gif
 
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BluberryPi said:
Hey, I am a new member, and I have a question. One of my favorite comic strip is foxtrot because it has so much physics:smile:! When I read this particular strip, however (7/30/2000- find it on Foxtrot GoComics) I was puzzled by the equations. Fortunately, 4 of them were printed in the Gocomics comments. Unfortunately, one was not really defined! Can someone please find this physics equation, explain it to me, and cite the source in which you got it from ? Thank You! The formula is in panel 4. By the way, the boy's name is Jason.http://api.ning.com/files/RlUkQ9Zps*RjiCqr6VvmdeH7x2Srx0GsPXjfQgGYD5GaS1MCjIQ6c7dIk0g4pZ7ZR5NDYsPIC6sq60J6WzrAiUBXxDattOV-/foxtrotplayground.gif
It is the equation of motion for a forced oscillator without daming.
 
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Thank you, Nasu! However, where did you get this from? I would like to know so I could go there.
 
Any book treating forced oscillation will have this. Or just look it up. It may be called "driven harmonic oscillator" or "forced h.o.".
Usualy the more general case, including damping is treated.
 
THANK YOU SOOOO MUCH! :smile::smile::smile::smile::smile::smile:
 
You also asked for an explanation. The formula gives the position ##x## of the oscillating object (in this case the kid on the horse). The interesting feature is the factor in the denominator ##(ω_o^2-ω^2)##.

##ω_o## is the natural frequency of oscillation of the system (the frequency of oscillation when the kid relaxes and doesn't force it to oscillate).

##ω## is the driving frequency (the frequency of the kid's pushes as he tries to increase the amplitude of the oscillations).

When these two frequencies match we have resonance (large amplitude oscillations).

##(ω_o^2-ω^2)## approaches zero as the two frequencies approach the same value, and since this factor is in the denominator, the value of the position increases and we have the large amplitude oscillations that characterize resonance.