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## PathSim Example of a spring-mass-damper system

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# IMPORTS ===============================================================================

import numpy as np

import matplotlib.pyplot as plt

from pathsim import Simulation, Connection

from pathsim.blocks import (

Integrator,

Amplifier,

Adder,

Scope

)

from pathsim.solvers import SSPRK33

# HARMONIC OSCILLATOR INITIAL VALUE PROBLEM =============================================

#initial position and velocity

x0, v0 = 2, 5

#parameters (mass, damping, spring constant)

m, c, k = 0.8, 0.2, 1.5

#blocks that define the system

I1 = Integrator(v0) # integrator for velocity

I2 = Integrator(x0) # integrator for position

A1 = Amplifier(c)

A2 = Amplifier(k)

A3 = Amplifier(-1/m)

P1 = Adder()

Sc = Scope(labels=["velocity", "position"])

blocks = [I1, I2, A1, A2, A3, P1, Sc]

#connections between the blocks

connections = [

Connection(I1, I2, A1, Sc),

Connection(I2, A2, Sc[1]),

Connection(A1, P1),

Connection(A2, P1[1]),

Connection(P1, A3),

Connection(A3, I1)

]

#create a simulation instance from the blocks and connections

Sim = Simulation(

blocks,

connections,

dt=0.1,

Solver=SSPRK33

)

# Run Example ===========================================================================

if __name__ == "__main__":

# Run the simulation for 30 seconds

Sim.run(duration=30)

# Plot the results directly from the scope

Sc.plot(lw=2)

Sc.plot2D(lw=2)

plt.show()