Maximum displacement of a coupled pendulum

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SUMMARY

The discussion focuses on the maximum displacements of a coupled pendulum system, specifically analyzing the relationship between the angular frequencies ω1 and ω2. The angular frequencies are defined as ω1 = √(g/l) and ω2 = √(g/l + 2k/m), where g represents gravitational acceleration, l is the length of the pendulum, k is the coupling constant, and m is the mass of the pendulum. Participants emphasize the need for a sketch to illustrate the motion of the system and clarify the variables involved.

PREREQUISITES
  • Understanding of coupled oscillators
  • Familiarity with angular frequency calculations
  • Knowledge of gravitational acceleration (g)
  • Basic principles of pendulum motion
NEXT STEPS
  • Explore the derivation of angular frequencies in coupled pendulum systems
  • Learn about the effects of coupling constants on oscillation behavior
  • Study the mathematical modeling of coupled oscillators
  • Investigate graphical representations of coupled pendulum motion
USEFUL FOR

Physics students, mechanical engineers, and anyone studying dynamics and oscillatory systems will benefit from this discussion.

Astrogirl101
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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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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\ ? ##
##\ ##
 

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