How to limit a function's cosine value as it approaches 0

Question

How do I get a cosine to peak up to a certain value as it hits 0? With the above code, the y-value peaks to infinity as it approaches 0.

import matplotlib.pyplot as plt
import numpy as np
amp = 1
time = np.linspace(-5, 5, 1000)
signal = np.cos(1 * np.pi * time) * abs(1/time)
plt.figure(figsize=(10, 10))
plt.ylim(-4, 4)
plt.plot(time, signal, color="black")
plt.savefig('output.png', bbox_inches='tight', pad_inches=0,
            transparent=True)

Put another way, based on my google-fu, how can I create a symmetrical exponentially decaying sinusoid with a maximum y-value as it approaches 0?

if you would like such a function described mathematically please consider posting your question on math.stackexchange or stackoverflow if this is a question about implementation — oW_, Sep 04 '20 at 03:49
Whoops, thanks! Thought about using math.stackexchange, but thought this would be better since it was numpy. Thanks for the clarification! — joaquincasares, Sep 04 '20 at 06:11

Ben · Accepted Answer · 2020-09-04T03:46:46.077

0

$\alpha e^{-\beta x^2}cos(x)$ where $\alpha$ is your peak and $\beta$ is proportional to the strength of the decay

This one's slightly longer and the peak is at $\alpha+1$ but the graph is easier to manipulate:
$cos(x)e^{-\beta x^2}+\alpha e^{-x^2}$

edited Sep 04 '20 at 03:46

answered Sep 04 '20 at 03:41

Ben

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That was perfect. Thanks!! – joaquincasares Sep 04 '20 at 06:13

How to limit a function's cosine value as it approaches 0

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