Maximum displacement of a coupled pendulum

In summary, the conversation is about finding the relationship between the maximum displacements of each pendulum for ω1 and ω2 and drawing a sketch to describe the motion of the system. The two angular frequencies ω1 and ω2 are given as ω1 =√(g/l) and ω2=√(g/l+2k/m), but it is mentioned that the length (l) does not appear in the problem statement. The other person asks for the work to be shared to understand how ω1 and ω2 were found.
  • #1
Astrogirl101
1
0
Homework Statement
How are the maximum displacements of each pendulum related for ω1 and ω2? Draw a sketch that describes the motion of the system in each case
Relevant Equations
ω1 =√(g/l)
ω2=√(g/l+2k/m)
Hi,
So I have this question to solve and I have no idea how to do it.
It states: ''How are the maximum displacements of each pendulum related for ω1 and ω2? Draw a sketch that describes the motion of the system in each case. ''
3Pq7H.png

The 2 angular frequencies that I have found are ω1 =√(g/l) and ω2=√(g/l+2k/m)
 
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  • #2
Hello Astrogirl, ##\qquad## :welcome: ##\qquad## !
Astrogirl101 said:
The 2 angular frequencies that I have found are ω1 =√(g/l) and ω2=√(g/l+2k/m)
Then you must know something we don't know, because ##l## doesn't appear in the problem statement.

Please post your work ! How did you find ##\omega_1## and ##\omega_2\ ? ##
##\ ##
 

What is the maximum displacement of a coupled pendulum?

The maximum displacement of a coupled pendulum refers to the furthest distance that the pendulums swing from their resting position when they are coupled or connected together.

What factors affect the maximum displacement of a coupled pendulum?

The maximum displacement of a coupled pendulum is affected by the length of each individual pendulum, the mass of the pendulums, and the strength of the coupling between the pendulums.

How does the maximum displacement change as the coupling strength changes?

As the coupling strength increases, the maximum displacement of the coupled pendulum also increases. This is because a stronger coupling allows for more energy to be transferred between the pendulums, resulting in larger swings.

What happens if the lengths of the pendulums are not equal?

If the lengths of the pendulums are not equal, the maximum displacement of the coupled pendulum will still occur, but it may not be symmetrical. The pendulum with the shorter length will swing further than the pendulum with the longer length.

Can the maximum displacement of a coupled pendulum be calculated?

Yes, the maximum displacement of a coupled pendulum can be calculated using a mathematical formula that takes into account the length, mass, and coupling strength of the pendulums. However, this calculation may be complex and may require advanced mathematical knowledge.

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