Murray at 18:47, 16 November 2024

2024-11-16T18:47:39Z

Murray: Created page with "{{Figure |Chapter=Dynamic Behavior |Figure number=5.1 |Sort key=501 |Figure title=Response of the damped oscillator to the initial condition x0 = (1, 0). |GitHub URL=https://g..."

2024-01-01T00:56:14Z

Created page with "{{Figure |Chapter=Dynamic Behavior |Figure number=5.1 |Sort key=501 |Figure title=Response of the damped oscillator to the initial condition x0 = (1, 0). |GitHub URL=https://g..."

New page

{{Figure
|Chapter=Dynamic Behavior
|Figure number=5.1
|Sort key=501
|Figure title=Response of the damped oscillator to the initial condition x0 = (1, 0).
|GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure-5.1-damposc_response.py
}}
[[Image:figure-5-1-damposc_response-time.png]]

'''Figure 5.1''': Response of the damped oscillator to the initial condition x0 = (1, 0). The solution is unique for the given initial conditions and consists of an oscillatory solution for each state, with an exponentially decaying magnitude.

<nowiki>
# damposc_response.py - dampled oscillator response
# RMM, 28 May 2023

import matplotlib.pyplot as plt
import numpy as np
import control as ct
import fbs # FBS plotting customizations

# Oscillator parameters
damposc_params = {'m': 1, 'b': 0.2, 'k': 1}

# System model (as ODE)
def damposc_update(t, x, u, params):
m, b, k = params['m'], params['b'], params['k']
return np.array([x[1], -k/m * x[0] - b/m * x[1]])
damposc = ct.NonlinearIOSystem(damposc_update, params=damposc_params)

# Simulate the response
tvec = np.linspace(0, 20, 100)
response = ct.input_output_response(damposc, tvec, 0, X0=[1, 0])

# Plot the states
fbs.figure('211')
plt.plot(response.time, response.states[0], 'b-')
plt.plot(response.time, response.states[1], 'b--')
plt.plot([response.time[0], response.time[-1]], [0, 0], 'k-', linewidth=0.75)
plt.xlabel('Time $t$ [s]')
plt.ylabel('States $x_1$, $x_2$')
plt.title(
"Response of the damped oscillator to the initial condition x0 = (1, 0)")
fbs.savefig('figure-5.1-damposc_response-time.png')
</nowiki>

@@ Line 26: / Line 26: @@
      m, b, k = params['m'], params['b'], params['k']
      return np.array([x[1], -k/m * x[0] - b/m * x[1]])
-damposc = ct.NonlinearIOSystem(damposc_update, params=damposc_params)
+damposc = ct.nlsys(damposc_update, params=damposc_params)
 # Simulate the response

Figure 5.1: Response of a damped oscillator - Revision history

Murray at 18:47, 16 November 2024

Murray: Created page with "{{Figure |Chapter=Dynamic Behavior |Figure number=5.1 |Sort key=501 |Figure title=Response of the damped oscillator to the initial condition x0 = (1, 0). |GitHub URL=https://g..."