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Math  /  Algebra

QuestionA mass attached to the end of a spring is set in motion. The mass is observed to oscillate up and down, completing 12 complete cycles every 6.00 s
What is the period TT of the oscillation? T=T= □\square s
What is the frequency ff of the oscillation? f=f= □\square Hz

Studdy Solution

STEP 1

1. The mass completes 12 complete cycles in 6.00 seconds.
2. The period T T is the time taken to complete one cycle.
3. The frequency f f is the number of cycles completed per second.

STEP 2

1. Calculate the period T T of the oscillation.
2. Calculate the frequency f f of the oscillation.

STEP 3

To find the period T T , use the formula for period, which is the total time divided by the number of cycles.
T=Total timeNumber of cycles T = \frac{\text{Total time}}{\text{Number of cycles}}

STEP 4

Substitute the given values into the formula.
T=6.00 s12 T = \frac{6.00 \, \text{s}}{12}

STEP 5

Calculate the period T T .
T=6.0012=0.50 s T = \frac{6.00}{12} = 0.50 \, \text{s}
The period of the oscillation is:
T=0.50 s T = 0.50 \, \text{s}

STEP 6

To find the frequency f f , use the formula for frequency, which is the number of cycles divided by the total time.
f=Number of cyclesTotal time f = \frac{\text{Number of cycles}}{\text{Total time}}

STEP 7

Substitute the given values into the formula.
f=126.00 s f = \frac{12}{6.00 \, \text{s}}

STEP 8

Calculate the frequency f f .
f=126.00=2.00 Hz f = \frac{12}{6.00} = 2.00 \, \text{Hz}
The frequency of the oscillation is:
f=2.00 Hz f = 2.00 \, \text{Hz}

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