How to calculate total power generated?

Question

I have a circuit with a piezoelectric transducer which converts mechanical energy to electrical. The ceramic is connected to a 1 Megaohm resistor and a voltmeter which reads voltage.

If I want to determine the power generated, do I just use P=V^2/R? And if so, how do I account for fluctuating voltage values? For example: 
I have the actual values of the voltages on a separate data table. How do I determine total power generated if voltage values are not the same? Do I do summation of power? Essentially, which voltage values do I choose to determine power?

Thank you very much! I appreciate it!

Christian Palma Almendáriz · Answer

If you have the voltage and time data pairs $(t, V(t))$ separated by a constant interval of time, eg:

$$(t_0,V_0), (t_0 +h=t_1,V_1), (t_0+2h=t_2,V_2)$$

You can use the trapezoidal rule to obtain the numerical value of:

$$  int_{t_0}^{t_f} V(t) approx dfrac{h}{2}(V(t_0)+2 sum_{k=0}^{N-1} V(t_i)+V(t_n )),$$  $h=dfrac{t_f-t_0}{N}, N=$your number of data pairs.

The mean value of V(t) is:

$$ bar{V}=dfrac{1}{t_f-t_0}int_0^{t_f} V(t)$$

Finally your mean value of P(t) is

$$  bar{P}=dfrac{bar{V}^2}{R}$$

How to calculate total power generated?

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