Investigating Resonance in Springs and Pendulums

Resonance is one of the most fascinating concepts in physics — when a system vibrates with maximum amplitude because it is driven at its natural frequency. Using springs and pendulums, students can observe resonance directly and understand why it is both useful and potentially destructive in the real world.

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The Experiment

Students set up a mass-spring system and a simple pendulum, each free to oscillate. A driver system (a mechanical vibrator or small motor) applies periodic forces at different frequencies. Lascells make a fantastic model for this, which is set up such that the strings are not tangled, and the experimental setup is immediately ready to go.

As the driving frequency changes, the amplitude of oscillation varies:

• At low or high frequencies, motion is small.

• At the natural frequency, amplitude increases dramatically — this is resonance.

The same can be shown using multiple pendulums of different lengths coupled by a thread; when one is set swinging, only the pendulum with the same natural frequency begins to move significantly.

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The Science

Resonance occurs when the frequency of a driving force matches the system’s natural frequency. Energy transfer is most efficient at this point, leading to a large increase in amplitude.

Key relationships:

$$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}} \quad \text{for a spring}$$ $$f = \frac{1}{2\pi}\sqrt{\frac{g}{l}} \quad \text{for a pendulum}$$

These equations show that the frequency depends on mass (for springs) and length (for pendulums).

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Skills Highlight

• Measuring oscillation frequency using timers or counting

• Plotting amplitude against driving frequency to identify resonance peaks

• Applying formulae to predict natural frequencies

• Understanding the practical implications of resonance in bridges, buildings, and musical instruments

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Why It Works in Teaching

Resonance links theory to experience — students can feel, hear, and see it. The rising amplitude at resonance provides an immediate visual and physical demonstration of a key principle of oscillatory motion, while the equations connect it back to quantitative analysis.