# How to estimate the frequency of the sample rate?

I'm studying for my class of physics laboratory and I need help with something:

Let's say I need to deduce the constant of elasticity of a spring and I will do it using a dual-range force sensor, throught dynamic and estatic measurements. So it is necessary to stablish the frecuency sample-rate according of the period that it will last my experiment. Considering that $F=n° of samples/T$ where $F$ is the frecuency, and the number of samples is one and $T$ is the period that last my experiment.

What do you recommend me to establish the period and frequency without really knowing a lot about the spring and its own characterstics? It should be through a simple and not necessarily precise way the estimation of the frecuency sample-rate.

• Per Nyquist, you need at least 2 samples per period (not 1 like you proposed) of whatever phenomenon you're measuring. Typically you want some higher multiple ("oversampling") like 4, 8, or 16x to conveniently be able to reconstruct the original signal. – The Photon Jun 25 '17 at 16:50
• Let's say I estimate the $T$ of the spring bouncing, and that is $1.2 s$ and I decide to get $30$ samples for second, then I will get a frecuency sample-rate of $25Hz$, don't you think is too little to get 25 points per second? I heard some friends used like $200Hz$. How can I justify mathematically and experimentally it is necessary to use that frecuency, for example? – Neisy Sofía Vadori Jun 25 '17 at 17:01
• Depends on the analysis you're going to do. I don't know what parameters you're going to try to estimate on the signal or what math you plan to apply to get there, so I can't give a complete answer. – The Photon Jun 25 '17 at 17:06
• I will estimate the constant of elasticity throught two different methods: one is dynamic, which means, I have to make the spring bouncing with a mass added to the extreme, and other, is static, whitout making the spring bouncing. And what I will do is measure the force in both cases with the instrument I specified, and then process the data in the origin. – Neisy Sofía Vadori Jun 25 '17 at 17:08

According to Nyquist's theorem, you cannot accurately measure the frequency of a signal unless you sample at least twice per period. For instance, if you are expecting a $\rm1\, Hz$ frequency, you must measure at least twice per second. However, if you are only measuring twice per second, a $\rm1.2\,Hz$ signal will be aliased and appear in your data like a $\rm0.8\,Hz$ signal. So in general you want to sample your signal more frequently than the minimum rate required by Nyquist's theorem.
• Do you think if I measure one oscillation of my spring (having stablished an specific length of elongation that I will mantain the whole process) and I observe in the software Motion DAQ how much aproximally last one period, in this case let's suppose: $1.2$ seconds and I arbitrary decide I want to get $200$ samples each period, so I will use a sample rate of $166Hz$ and I justify this by saying that I stablished that amount of samples because I wanted to reconstruct the original signal and reduce the noise properly, will be enough as justification? – Neisy Sofía Vadori Jun 25 '17 at 18:13