You may (should!) have noticed that something is not right with the Euler model of your hanging oscillator. Describe in detail the artificial behavior you observe in your model, and explain why it doesn’t represent a realistic oscillating mass. Recall that in the Euler method, the accuracy of the solution can be increased by using a smaller value of Δt. Can you get rid of the artificial behavior by making Δt smaller?

Euler's method we are approximating the solution to a line

In summary The description improves when the pitch is smaller, spring displacement is small

Explanation:

In the experiment of this problem we have one more pendant of a spring, which is oscillating in a simple harmonic motion. To describe this movement, the period of oscillation can be measured and related to the properties of the spring and the applied mass.

                w = Rak / m

                w 02pi f = 2pi / T

                T = 2pi Ra m / k

Dende the period is average as the time that the body takes to give a complete oscillation, to decrease the error in general several oscillations are measured together,

When we use Euler's method it consists of approximating the equation to a line, finding the slope and with this calculating our value of interest, this method is strongly dependent on the passage of time that is used.

In our case the equation that represents the movement is

         d²x / dt² = -w² x

 By using Euler's method we are approximating the solution to a line or a series of lines depending on the time jump used, and the solution analytically which is a cosine. As the step is higher, the greater the discrepancy between the line and the cosine, note that the same starting point has them.

 If we expand the cosine function in a Taylor series

         cos tea = 1 - θ² / 2! + θ⁴ / 4! -…

we see that if the angle is small we can only leave the first two terms

Now we decrease the step in the Euler method, which is why we get closer and closer to this expanded function, which is why our description of the experiment is better, the time and positions are more similar to those measured, but the step has to be very small since the cocene function is quadratic

In summary The description improves when the pitch is smaller, spring displacement is small

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y