Solving Pendulum Confusion: m*a=-k*x Explained

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Discussion Overview

The discussion revolves around the equation of motion for a pendulum, specifically the relationship expressed as m*a = -k*x, and the implications of the negative sign in this context. Participants explore the dynamics of a pendulum's motion, particularly focusing on the restoring force and its direction relative to displacement from equilibrium.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the validity of m*a = -k*x, questioning the meaning of the negative sign and suggesting that the relationship might need to account for directionality differently.
  • Another participant asserts that m*a represents the restoring force, emphasizing that its direction is opposite to the displacement from equilibrium.
  • A later reply reinforces the previous point, acknowledging the clarity provided by the explanation and expressing relief at understanding the concept.
  • Another participant discusses the equation of motion for a pendulum with small amplitude, providing a detailed breakdown of the forces involved, including the role of gravitational acceleration and how it relates to angular displacement.
  • This participant notes that the negative sign arises because gravitational force acts to restore the pendulum towards its equilibrium position, regardless of the bob's position.

Areas of Agreement / Disagreement

Participants exhibit some agreement on the nature of the restoring force and its relationship to displacement, but there remains confusion regarding the initial expression m*a = -k*x and its implications, indicating that the discussion is not fully resolved.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the pendulum's motion, particularly in terms of amplitude and the definitions of the forces involved. The relationship between angular displacement and gravitational force is also not fully explored.

LLT71
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I find it somehow confusing to imagine why m*a=-k*x is "generally valid". that minus sign bothers me. Imagine I raised a bob to some height (ex. from the left side) and then released it. from that moment till the moment where it reaches equilibrium position m*a and restoring force have same direction. from a moment where it "goes of" the equilibrium position to the moment when it reaches the same height on the right side m*a and restoring force have different direction and so on. should it be m*a=+-k*x? what I'm missing?
 
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##ma## IS the restoring force. The direction is opposite from the displacement from equilibrium
 
BvU said:
##ma## IS the restoring force. The direction is opposite from the displacement from equilibrium
god I feel so stupid... thanks that was straight forward!
 
No need to feel stupid. It looked convincing ! And: you are welcome.
 
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for a pendulum with small amplitude: the equation of motion is approximately: mass* length^2 *angular acceleration = - mass * gravitational acceleration * length * angle.

the k does not come in. the restoring torque is - mass * gravitational acceleration * length * angle. The magnitude of the restoring force is: mass * gravitational acceleration. The - sign come in because the gravitational acceleration is always downward, and acts to close the angle theta. if the bob is on the left hand side, for example theta is less than zero and the force acts to increase theta. If the bob is on the right hand side, theta is greater than zero, and the gravitational force acts to decrease theta. the gravitational force always acts against the angular displacement theta.
 
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