A vertical spring scale can measure weights up to 225 N . The scale extends by an amount of 12.5 cm from its equilibrium position at 0 N to the 225 N mark. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.65 Hz. Ignoring the mass of the spring, what is the mass m of the fish?

The mass of the fish is 6.493 kilograms.

Explanation:

The spring-mass system experiments a Simple Harmonic Motion, then the angular frequency (), in radians per second, is determined by the following equation:

(1)

Where is the frequency, in hertz.

In addition, the mass of the fish (), in kilograms, is:

(2)

Where is the spring constant, in newtons per meter.

And the spring constant is determined by Hooke's Law:

(3)

Where:

- Elastic force, in newtons.

- Spring elongation, in meters.

If we know that , and , then the mass of the fish is:

The mass of the fish is 6.493 kilograms.

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