Final answer:
The frequency of small oscillations is found by taking the reciprocal of the period, with the formula f = 1/T.
If the frequency is known, the period can be calculated by T = 1/f.
Examples include medical devices, musical instruments, and automotive suspensions.
Step-by-step explanation:
To find the frequency of small oscillations, you can utilize the relationship between frequency (f) and the period (T).
The frequency is the reciprocal of the period, given by the formula f = 1/T.
For example, if an ultrasound device oscillates with a period of 0.400 µs, the frequency of oscillation is f = 1 / (0.400 × 10-6s), which calculates to 2.5 MHz.
Conversely, if you know the frequency, you can determine the period of oscillation by rearranging the formula to T = 1/f.
For instance, middle C on a musical instrument has a frequency of 264 Hz, the time for one complete oscillation, or the period, is T = 1 / 264 Hz, which is approximately 3.79 ms.
Further examples include calculating the frequency of a tuning fork or the oscillation frequency of a car with bad shock absorbers.
In cases of complex systems or changing conditions, like varying mass or tension in a string, different formulas or modifications to the base formula may be necessary to accurately determine the frequency or period.