Question

You are looking at a small, leafy tree. You do not notice any breeze, and most of the leaves on the tree are motionless. One leaf, however, is fluttering back and forth wildly. After a while, that leaf stops moving and you notice a different leaf moving much more than all the others. Explain what could cause the large motion of one particular leaf.

Short answer

The resonance of the leaf is set by the frequency of the driving force not by the size. So when the frequency starts to change then the leaf begins to oscillate into resonant frequency.

Step-by-step solution

Relationship between Frequency and amplitude

If an oscillator is subject to a sinusoidal driving force that is described by

$F\left(t\right)=F_0\sin \omega t$

It exhibits resonance, in which the amplitude is largest when the driving frequency matches the natural frequency ${\omega }_0=\sqrt{\frac{k}{m}}$of the oscillator.

${\omega }_0=$Resonance frequency

Step 2:  Explain what could cause the large motion of one particular leaf

A breeze that cause a flag to flap over the edge of a leaf produces fluttering. A restoring torque can be provided by the fibers in its stem. The leaf is driven by a large amplitude resonance vibration if the breeze’s frequency matches with one particular leaf’s natural frequency. So we can conclude that the resonance of the leaf is set by the frequency of the driving force not by the size. So when the frequency starts to change then the leaf begins to oscillate into resonant frequency.