toyexample_simple.md

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(python_by_example)=

A Toy Example

We will start off by considering a toy example of tossing a coin and eventually add air resistance etc. Let us begin by writing down the velocity and displacement equations of a point mass object thrown vertically above the ground with an initial velocity $u_0$.

Under the effect of gravity, the velocity of the object at any time instant from start($t=0$) is given by

$ v_t = u_0 + gt $

where $g$ represents acceleration due to gravity $\sim 10 \frac{m}{s^2}$

Also, the displacement covered by the point mass is given by

$ s_t = u_0t + \frac{1}{2}gt^2 $

(whileloopprog)=

ts_length = 100
ϵ_values = []
i = 0
while i < ts_length:
    e = np.random.randn()
    ϵ_values.append(e)
    i = i + 1
plt.plot(ϵ_values)
plt.show()