If a change in speed “Δv” occurs and the mass starts at rest, would the change in speed also equal the final speed of the mass?

Yes, if the mass starts at rest, the change in speed will be equal the final speed, because:

Δv = Vf - Vo

How Vo (Initial velocity) is equal zero, we simplificate:

Δv = Vf

Then, the change of the speed, if the mass starts at rest, will be equal to final velocity.

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explanation:

as the height from which the ruler was dropped increased, the speed of the ruler at ryan's hand increased.

resonant frequency