[Paper Review] Resonance in Putting

Robert D. Grober|ArXiv.org|Mar 10, 2009

Sports Dynamics and Biomechanics3 citations

TL;DR

This paper proposes that elite golf putting strokes function as a pendulum driven at twice its natural frequency, minimizing speed errors from force variations. The resonance model explains why top players adopt this stroke style, offering a physics-based rationale for its effectiveness in reducing putting inconsistency.

ABSTRACT

It is shown that the putting stroke of world class golfers can be described as the motion of a pendulum driven at twice its natural resonance frequency. This model minimizes error in the speed of the putter head due to random errors in the magnitude of the applied forces, providing rational for why great players have developed this particular putting stroke.

Motivation & Objective

• To understand the physical mechanism behind consistent putting in elite golfers.
• To investigate why certain putting strokes minimize speed errors despite force variability.
• To model the putting stroke as a driven pendulum system to identify optimal dynamics.
• To provide a physics-based explanation for the prevalence of a specific putting technique among top players.

Proposed method

• Model the putting stroke as a driven pendulum with a periodic force applied at twice the pendulum's natural frequency.
• Use classical mechanics to derive equations of motion for the driven pendulum system.
• Analyze the system's response to random perturbations in force magnitude to assess error minimization.
• Compare the model's error sensitivity to alternative driving frequencies.
• Validate the model by aligning its predictions with observed putting dynamics in professional golfers.
• Apply resonance theory to demonstrate that driving at 2ω minimizes sensitivity to force errors.

Experimental results

Research questions

• RQ1 Why do elite golfers exhibit such consistent putting speed despite variable force application?
• RQ2 How does driving a pendulum-like system at twice its natural frequency affect error sensitivity?
• RQ3 What physical principle explains the observed consistency in professional putting strokes?
• RQ4 Can the putting stroke be modeled as a driven pendulum system that minimizes speed errors?
• RQ5 Is there an optimal driving frequency that reduces sensitivity to random force variations in the putting motion?

Key findings

• The putting stroke of world-class golfers closely matches a pendulum driven at twice its natural frequency (2ω).
• This driving frequency minimizes speed errors caused by random variations in the applied force.
• The model shows that 2ω driving produces the lowest sensitivity to force perturbations, explaining its dominance in elite play.
• The system's resonance behavior at 2ω provides a physical basis for the consistency observed in professional putting.
• The findings suggest that the human motor system may naturally converge on this optimal frequency for minimizing performance errors.
• The model offers a quantitative explanation for why this specific putting technique is favored by top players.