Arange demo with oscillation

Oscialltion

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
sns.set()

$$ Y = Asin(\omega t + \phi )$$

fs = 100
ts = np.arange(0,60,1/fs)
ts

array([0.000e+00, 1.000e-02, 2.000e-02, ..., 5.997e+01, 5.998e+01,
       5.999e+01])

np.sin(ts)

array([ 0.        ,  0.00999983,  0.01999867, ..., -0.27610536,
       -0.28570267, -0.29527141])

freq = 0.5
ts*(2*np.pi*freq)

array([0.00000000e+00, 3.14159265e-02, 6.28318531e-02, ...,
       1.88401311e+02, 1.88432727e+02, 1.88464143e+02])

Single oscillation

fs = 100
ts = np.arange(0,60,1/fs)
amp = 1.0
freq = 0.025

'''initialize figure'''
plt.figure(figsize = [20,4])

'''create oscillation:  Y = Asin(wt)| w = 2.pi.f'''
ys = amp*np.sin(ts*(2*np.pi*freq))

lb = "amp: " + str(amp) + ",freq:" + str(freq)   
plt.plot(ts,ys, label = lb)

plt.xlabel("Time in seconds") 
plt.ylabel("Displacement")
plt.legend()
plt.show()

Variable Amplitude and Frequency in Oscillation

fs = 100
ts = np.arange(0,60,1/fs)
'''initialize figure'''
plt.figure(figsize = [20,6])

'''iterate over each amplitude and 
frequency and create a oscillation plot'''

for i in range(1,10):
    amp = 100*1/float(i)
    freq = 0.025*i

    '''Y= A sin(wt) | w = 2*pi*f'''
    ys = amp*np.sin(ts*2*np.pi*freq)

    lb= "amp: "+str(amp)[0:4] + ",freq:"+str(freq)[0:4]
    plt.plot(ts,ys,label=lb )

plt.xlabel("Time in seconds") 
plt.ylabel("Displacement")
plt.legend()
plt.show()

Superposition of oscillations

fs = 100
ts = np.arange(0,60,1/fs)

'''initialize figure'''
plt.figure(figsize = [20,6])

'''define 10 different amplitudes and frequencies'''
amps = [1*1/float(i) for i in range(1,10)]
freqs = [0.025*i for i in range(1,10)]

'''List comprehension: '''
ys = sum([amp*np.sin(ts*2*np.pi*freq) for amp,freq in zip(amps,freqs)])

'''create a plot'''
plt.plot(ts,ys, label= "Superposed oscillation")
plt.legend()
plt.show()

Is this a sawtooth wave?

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Assignment:

1. Write python function for creating a random oscialltion with amplitude in range (1,5) and frequency in range (0.25,1)
2. Create 20 different oscillations by implementing python function defined above and implement superposition principle to obtain single resultant oscillation.

def oscillator():
    '''implement y = Asin(wt)+Bcos(wt) with random
    amplitude in (1,5) and freq in (0.25,1)'''