Recent content by roam

Thank you so much for all the explanations. I have only one more follow up question. In post #16 I used one of the kinematic equations to find the "initial vertical velocity": ##y-y_{0}=v_{y}t+\frac{1}{2}at^{2}## ##9-0=v_{y}(4.5)+\frac{1}{2}(-9.81)(4.5)^{2}## ##\therefore v_{y}\approx\ 24...

Hi @PeroK and @Steve4Physics, Thank you so much for your inputs. I believe the equation to use is: ##y-y_0 = v_{y} t + \frac{1}{2} a t^2 \tag{1}## Is this right? If so, the initial y velocity becomes: ##9 = v_{y} (4.5) + \frac{1}{2} (9.81) (4.5)^2 \implies v_{y} \approx -20 \ \text{m/s}##...

Hi there, I'm not sure, do you mean ##v^2_y = v_{0y}^2 -2a(y-y_0)##? In that case, we have ##v^2_y = v_{0y}^2 -2 (9.81) \times 9##. That is as far as we could go with this equation. P.S. The final height of the projectile is 9m. Hi there, By initial launch velocity do you mean ##v_{oy} =...

I am trying to find the launch angle ##\theta## using the relationship: ##\theta=\arctan(\frac{v_{y}}{v_{x}})## So, ignoring attenuation due to air resistance, we have a constant horizontal velocity: ##v_x = d_x/t = 95m/4.5s \approx 21 m/s## But what value do we use for ##v_y## which is not...

I have generated a distribution (normalized such that the sum is equal to 1) by using the code: M=500; % Number of samples z=1; SUM = 1; ns = rand(1,M).^z; % random numbers TOT = sum(ns); X = (ns/TOT)*SUM; % Re-scaling hist(X(1,:),100) For an exponent ##z=1##, the sampling distribution is...

Hi @Stephen Tashi Central Limit Theorem does tell us that the standard deviation of the modulation depth decreases as ##N## increases. That means that the sum gets progressively flatter as ##N## gets larger (according to an inverse square-root law). So, can't we also argue that the Central...

If I understood correctly, you are suggesting that as N increases, the value for each variable converges to the expected value, which is the mean value that the underlying function takes. This is basically a definition of the (strong) Law of Large Numbers. The central limit theorem simply...

But this is a different problem. If we add up a large number of curves with random phases (this could be any function; even sine waves), the sum tends to flatten out. Is this in consequence of the Law of Large Numbers, CLT, or a different law? There has to be a rigorous explanation of this...

Hi @RPinPA Do you think it is possible to argue that the result is a consequence of the Central Limit Theorem?

Hi FactChecker, It works perfectly. Thank you so much for your time. P.S. How did you choose the optimal value for the jump tolerance?

Thanks for all the suggestions. I tried the method suggested by @DaveE and @George Jones and used atan2. But I am still not quite getting the correct plot. Here is the result (yellow line): The problem is that, the plot should not take the form of a staircase function. Unlike the two other...

The function that I am plotting is known as the "Airy function" which gives the output of a Fabry-Perot etalon. The dips occur whenever ##\varphi=2\pi q##, for ##q## being an integer. The period is known as the "free spectral range". The horizontal axis is the frequency ##\nu## which is...

Here is a picture of these plots from a paper: When I try to reproduce the 3rd graph above (yellow line below), I get sharp discontinuities: Those jump discontinuities should not occur, and the function should never rise to the high value of the two other plots. So, what could be the cause...

Hi @RPinPA So, how do we explain why the mean of the population at all different points tend to a similar value as ##n \to \infty##? Is that just something we know a priori from the Law of Large Numbers? I am looking for a rigorous explanation of why the sum curve gets flatter. Intuitively I...

Hi @RPinPA Do you know how the Law of Large Numbers might be applicable to this situation? Does the law say that the sum of all those independent random values must approach a specific value? Yes, all the individual signals are periodic. But the periods are slightly differ from each other...