A mass m at the end of a spring vibrates with a frequency of 0.72 Hz . When an additional 700 g mass is added to m, the frequency is 0.64 Hz . Part A What is the value of m? Express your answer using two significant figures.

The value of m is 2635.294 grams.

Explanation:

Let suppose that mass-spring system has a simple harmonic motion, to this respect the formula for frequency is:

Where is the angular frequency, measured in radians per second.

For a mass-spring system under simple harmonic motion, the angular frequency is:

Where:

- Spring constant, measured in newtons per meter.

- Mass, measured in kilograms.

The following equation is obtained after replacing angular frequency in frequency formula:

As this shows, frequency is inversely proportional to the square root of mass. Hence, the following relationship is deducted:

If , and , the resulting expression is simplified and then initial mass is found after clearing it:

The value of m is 2635.294 grams.

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