Solve Unknown Spring Equation from Foxtrot Comic Strip

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In summary, the conversation is about the physics equations featured in a Foxtrot comic strip and a user is seeking an explanation and source for one of the equations. Another user provides the equation and an explanation of its significance in forced oscillations and resonance. The conversation also points out a mistake in the equation in the first panel.
  • #1
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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  • #2
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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  • #3
Thank you, Nasu! However, where did you get this from? I would like to know so I could go there.
 
  • #4
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.
 
  • #6
THANK YOU SOOOO MUCH! :smile::smile::smile::smile::smile::smile:
 
  • #7
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.
 
  • #8
By the way, the equation in first panel has a mistake in it. Can you spot it?:)
 
  • #9
Oh yeah! That author knows better than to make a unit mismatch!
 

Related to Solve Unknown Spring Equation from Foxtrot Comic Strip

1. How do you solve the unknown spring equation from the Foxtrot comic strip?

To solve the unknown spring equation from the Foxtrot comic strip, you will need to use the equation F = -kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement from the equilibrium position. You will also need to know the mass of the object attached to the spring, as well as any other relevant variables.

2. What is the purpose of solving the unknown spring equation from the Foxtrot comic strip?

The purpose of solving the unknown spring equation from the Foxtrot comic strip is to calculate the force required to stretch or compress a spring to a certain length or distance. This can be useful in various applications, such as designing springs for different purposes or understanding the behavior of objects attached to springs.

3. What is the significance of the Foxtrot comic strip in relation to the unknown spring equation?

The Foxtrot comic strip often features math and science concepts, including physics. In this particular comic strip, the character Jason is using the unknown spring equation to calculate the force required to launch a water balloon at his sister. It serves as a fun and relatable way to introduce and demonstrate the use of this equation.

4. Are there any real-life applications for the unknown spring equation from the Foxtrot comic strip?

Yes, there are many real-life applications for the unknown spring equation. It is commonly used in engineering and design to determine the force needed to compress or stretch a spring to a specific length. It is also used in physics experiments and research to study the behavior of objects attached to springs.

5. Can the unknown spring equation from the Foxtrot comic strip be used for any type of spring?

Yes, the unknown spring equation can be used for any type of spring, as long as the spring is linear (follows Hooke's Law) and the other relevant variables are known. This includes springs made of various materials and with different shapes and sizes. However, it may not be applicable for non-linear springs, which do not follow Hooke's Law.

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