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undamped_oscillator.py
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# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd
def simulation(
sim_time=5.0,
delta_t=0.01,
mass=0.2,
spring_constant=10,
unweighted_length=1.000,
init_displacement = 0.3,
method="forward",
):
gravity_acceleration = -9.81
sim_steps = int(sim_time / delta_t)
weight = mass * gravity_acceleration
weight_displacement = np.abs(mass * gravity_acceleration) / spring_constant
weighted_length = unweighted_length + weight_displacement
if method == "forward":
simulation_df = forward_euler(
spring_constant=spring_constant,
unweighted_length=unweighted_length,
weighted_length=weighted_length,
init_displacement=init_displacement,
mass=mass,
weight=weight,
sim_steps=sim_steps,
delta_t=delta_t,
)
elif method == "midpoint":
simulation_df = midpoint_euler(
spring_constant=spring_constant,
unweighted_length=unweighted_length,
weighted_length=weighted_length,
init_displacement=init_displacement,
mass=mass,
weight=weight,
sim_steps=sim_steps,
delta_t=delta_t,
)
elif method == "leapfrog":
simulation_df = leapfrog(
spring_constant=spring_constant,
unweighted_length=unweighted_length,
weighted_length=weighted_length,
init_displacement=init_displacement,
mass=mass,
weight=weight,
sim_steps=sim_steps,
delta_t=delta_t,
)
return simulation_df
def forward_euler(
spring_constant,
unweighted_length,
weighted_length,
init_displacement,
mass,
weight,
sim_steps,
delta_t,
):
length = weighted_length + init_displacement
velocity = 0
trace = [[0, length, 0]]
for step_index in range(1, sim_steps + 1):
restoring_spring_force = spring_constant * (length - unweighted_length)
total_force = restoring_spring_force + weight
acceleration = total_force / mass
length += -velocity * delta_t
velocity += delta_t * acceleration
trace.append([step_index, length, velocity])
simulation_df = pd.DataFrame({
"time": [x[0] * delta_t for x in trace],
"length": [x[1] for x in trace],
"velocity": [x[2] for x in trace],
"method": "forward_euler",
})
return simulation_df
def midpoint_euler(
spring_constant,
unweighted_length,
weighted_length,
init_displacement,
mass,
weight,
sim_steps,
delta_t,
):
length = weighted_length + init_displacement
velocity = 0
trace = [[0, length, 0]]
for step_index in range(1, sim_steps + 1):
velocity_old = velocity
acceleration = (spring_constant * (length - unweighted_length) + weight) / mass
velocity_half_step = velocity_old + acceleration * (delta_t / 2)
length_half_step = length - velocity_old * (delta_t / 2)
acceleration_half_step = (spring_constant * (length_half_step - unweighted_length) + weight) / mass
velocity += acceleration_half_step * delta_t
length += -velocity_half_step * delta_t
trace.append([step_index, length, velocity])
simulation_df = pd.DataFrame({
"time": [x[0] * delta_t for x in trace],
"length": [x[1] for x in trace],
"velocity": [x[2] for x in trace],
"method": "midpoint_euler",
})
return simulation_df
def leapfrog(
spring_constant,
unweighted_length,
weighted_length,
init_displacement,
mass,
weight,
sim_steps,
delta_t,
):
length = weighted_length + init_displacement # m
acceleration = (spring_constant * (length - unweighted_length) + weight) / mass
velocity = 0 - acceleration * delta_t / 2
trace_length = [[0, length]]
trace_velocity = [[0, velocity]]
for step_index in range(1, sim_steps + 1):
restoring_spring_force = spring_constant * (length - unweighted_length)
total_force = restoring_spring_force + weight
acceleration = total_force / mass
velocity += delta_t * acceleration
length += -velocity * delta_t
trace_length.append([step_index, length])
trace_velocity.append([step_index, velocity])
simulation_df = pd.merge(
pd.DataFrame({
"time": [x[0] * delta_t for x in trace_length],
"length": [x[1] for x in trace_length],
"method": "leapfrog",
}),
pd.DataFrame({
"time": [(x[0] - 0.5) * delta_t for x in trace_velocity],
"velocity": [x[1] for x in trace_velocity],
"method": "leapfrog",
}),
how="outer",
)
return simulation_df