Differential Eq. for Spring-Mass System on Seesaw: Case 1 & 2

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SUMMARY

The discussion focuses on deriving the differential equations for a spring-mass system on a seesaw, specifically in two cases. In Case 1, a single spring with spring constant K1 is attached to a balanced seesaw with total mass M, leading to oscillations around the pivotal point. In Case 2, two springs with constants K1 and K2 are attached at both ends of the seesaw, complicating the system's dynamics. The key to solving these cases lies in understanding the equations of motion for simple harmonic motion and applying superposition principles.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with spring-mass systems and Hooke's Law
  • Knowledge of simple harmonic motion
  • Basic principles of mechanics related to oscillations
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  • Study the derivation of the differential equation for a simple mass-spring system
  • Research the concept of superposition in oscillatory systems
  • Explore the dynamics of coupled oscillators
  • Learn about the effects of varying spring constants on system behavior
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Tahir Mushtaq
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case 1: Seesaw is balanced with its fulcrum point or pivotal point. At one end of seesaw, the spring (with spring constant K1) is attached. Now the seesaw has total mass M which is attached to spring, form a spring-mass system. I confuse on this point that the oscillation of seesaw will be around pivotal point. Then what is differential equation of spring-mass system.

case 2: The same case with both ends of Seesaw is attached with springs having spring constant K1 and K2. Then what is differential equation of this system.
 
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1) What equations would be relevant to this problem?

2) What have you tried to do to solve it so far?

3) Hint: Can you derive an Equation of Motion for a simple mass-spring system (without a seesaw)? If so, can you consider the motion of the seesaw with the mass-spring system as a superposition of simple harmonic motion?

I cannot visualize your seesaw-spring system. If you can describe it better (or link to a picture), maybe I can help more.
 

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