Question

I was wondering that, if the duration of a recurring event varies as time goes on, what would the magnitude of this quantity be measured in? For instance, if the time for an oscillation of a weighted spring decreases (because of energy loss to resistance etc.) by one second every 5 seconds (just picking arbitrary numbers), what would the unit of this rate of change be? If the duration is measured in seconds, the derivative with respect to time would be in terms of t/t or seconds per second which equates to no unit and obviously doesn't make sense and cannot be correct.

So I'm basically asking if I'm missing something that makes the unit not t/t or otherwise does this quantity actually not make sense and how come?

Answer 1

The rate of change of an oscillation period is measurable; it can be expressed as seconds per second (s/s) which may simplify to a rate such as -0.2 s/s, representing a decrease or damping of the oscillation period over time.

Step-by-step explanation:

When considering the rate at which the duration of an oscillating system like a weighted spring changes, one must understand that this rate is indeed measurable and has appropriate units. If the oscillation time decreases by one second every five seconds, the rate of change is -1 second per 5 seconds, which simplifies to -0.2 seconds per second (s/s).

However, to express this concept in physics, we typically use the concept of damping or decay rate, usually given in inverse seconds (1/s or s-1). Although the unit 'seconds per second' might seem to cancel out, it is indeed correct and signifies how much the period of the oscillation changes for each second of elapsed time.

In physics, the unit for the rate of change of a recurring event would depend on the specific quantity being measured. For example, if the time for an oscillation of a weighted spring decreases, the rate of change can be measured in units of time per time, such as seconds per second (s/s).

While this may seem unusual, it represents a change in the duration per unit time. This quantity does make sense and is used in physics to express rates of change in recurring events.