A mass oscillates on the end of a spring with a period of 4.0 seconds. What is the frequency of the oscillator?

Answer 1

This sounds like a homework question, so rather than doing your homework for you, I'll explain how to find the answer for yourself.

The period and the frequency are very easy to find from the information provided. First, remember the definitions of period and frequency:

Period is the amount of time per oscillation.
Frequency is the number of oscillations per unit time.

When you see the word "per" in these definitions, you should think division, because that is how you find the answer. When we say period is time per oscillation, this means time divided by oscillations. So your period is obtained by dividing the amount of time (in seconds) by the number of oscillations in that time. The units will make sense this way too: time divided by oscillations will give you a number that means seconds PER oscillation, which is what period is!

Similarly, frequency is oscillations per time, so take the number of oscillations and divide it by the number of seconds it took. Your units will be oscillations per second, which makes sense for a measure of frequency.

Answer 2

The period of an oscillation is the time per cycle of that movement. The frequency of the oscillation is the number of cycles per unit of time for that movement. Lastly, period is the inverse of frequency, and vice versa. Let's work this one. Period = 4 seconds per cycle = 4 sec/cycle Frequency = 1/period = 1/(4 sec/cycle) = 1 cycle/4 seconds A frequency of 1 cycle/ 4 seconds is 1/4 cycle per second or 15 cycles per minute.