Quantify measure of oscillation and amplitude in time-series data

Let's define a term, score, as a metric that measures the extent of oscillation by incorporating information about amplitude and frequency. High score means that big oscillations happen frequently. Low score means that small oscillations happen intermittently.

Compare Set 1 and Set 2. They have the same amplitude, but has different frequency, making set 1 to have lower score=2.1 then set 2 score=4.

I want to come up with a metric that allows me to quantify the score. I was thinking of taking derivatives, sum them up, and divide by the total number of points:

But I don't think this is going to work because the absolute difference amplitudes of two points depends on when I sampled them. Furthermore, my data has uneven sampling rate, which makes $$\Delta t_i$$ non-uniform.

How should I do?

$$y_t = \beta_0 + \sum_{frq=0}^n \beta_{frq} \cdot f_{frq}(t)$$
where $$f_{frq}(t) = sin(2\pi \cdot frq \cdot t)$$
the size of coefficients $$\beta$$ could then be used to approximate the score you are interested in. This approach also overcomes the irregular sampling as you only need to evaluate each sine wave at the points where you have data.