Damped oscillators are common in engineering. This challenge will help you automate their simulation and analysis. When a mass is attached to a spring and damper, its motion is governed by the balance of restoring, damping, and inertial forces. For underdamped systems, the displacement follows a characteristic exponentially decaying oscillation, which is important for predicting how real-world mechanical systems behave after being disturbed.


import unittest
import user_code
import ast
import re   
import importlib
import csv
import unittest
import importlib
import math

class TestTask(unittest.TestCase):
    def test_returns_list_with_correct_length(self):
        import user_code
        importlib.reload(user_code)
        duration = 1.0
        dt = 0.1
        expected_length = int(duration / dt) + 1
        result = user_code.damped_oscillator_displacement(1.0, 10.0, 1.0, 1.0, 0.0, duration, dt)
        _dynamic_test(
            self,
            isinstance(result, list) and len(result) == expected_length,
            f"Returned list has correct number of elements: {expected_length}",
            f"Expected list of length {expected_length}, got {len(result) if isinstance(result, list) else 'not a list'}",
        )

    def test_initial_displacement(self):
        import user_code
        importlib.reload(user_code)
        x0 = 1.5
        result = user_code.damped_oscillator_displacement(1.0, 10.0, 1.0, x0, 0.0, 1.0, 0.05)
        _dynamic_test(
            self,
            isinstance(result, list) and len(result) > 0 and math.isclose(result[0], x0, abs_tol=1e-9),
            "First value equals initial displacement x0",
            f"Expected first value {x0}, got {result[0] if isinstance(result, list) and len(result) > 0 else result}",
        )

    def test_amplitude_decreases(self):
        import user_code
        importlib.reload(user_code)
        # Use a clear underdamped case
        m = 1.0
        k = 10.0
        c = 1.0
        x0 = 2.0
        v0 = 0.0
        duration = 2.0
        dt = 0.05
        result = user_code.damped_oscillator_displacement(m, k, c, x0, v0, duration, dt)
        _dynamic_test(
            self,
            isinstance(result, list) and len(result) >= 3,
            "Function returns a list with at least 3 values",
            f"Expected at least 3 values, got {len(result) if isinstance(result, list) else 'not a list'}",
        )
        # Check that the envelope (absolute value) decreases over time
        abs_vals = [abs(x) for x in result]
        decreasing = all(y <= x + 1e-8 for x, y in zip(abs_vals, abs_vals[1:])) or all(y < x for x, y in zip(abs_vals, abs_vals[1:]))
        # However, since oscillations, check if the max of the second half is less than max of first half
        half = len(abs_vals) // 2
        max1 = max(abs_vals[:half])
        max2 = max(abs_vals[half:])
        _dynamic_test(
            self,
            max2 < max1,
            "Oscillation amplitude decreases over time (damping present)",
            f"Expected amplitude to decrease, but max in second half ({max2}) not less than first half ({max1})",
        )

    def test_various_parameters(self):
        import user_code
        importlib.reload(user_code)
        # Try a different set of parameters
        m = 2.0
        k = 20.0
        c = 2.0
        x0 = 0.5
        v0 = 0.2
        duration = 2.0
        dt = 0.2
        result = user_code.damped_oscillator_displacement(m, k, c, x0, v0, duration, dt)
        _dynamic_test(
            self,
            isinstance(result, list) and len(result) == int(duration/dt)+1,
            "Function handles different parameters and returns correct length list",
            f"Expected list of length {int(duration/dt)+1}, got {len(result) if isinstance(result, list) else 'not a list'}",
        )
        # Check that the first value is x0
        _dynamic_test(
            self,
            math.isclose(result[0], x0, abs_tol=1e-9),
            "First value matches initial displacement for different parameters",
            f"Expected {x0}, got {result[0] if isinstance(result, list) and len(result) > 0 else result}",
        )

def _dynamic_test(test_case, condition, success_message, failure_message):
    if condition:
        test_case._testMethodName = success_message
        test_case.assertTrue(True, success_message)
    else:
        test_case._testMethodName = failure_message
        test_case.fail(failure_message)

def normalize_text(text):
    text = text.lower()
    text = re.sub(r"\\s{2,}", " ", text)
    text = re.sub(r"\\s*([,:?])\\s*", r"\\1 ", text)
    return text.strip()

def change_var(code: str, var_name: str, value: str) -> str:
    tree = ast.parse(code)
    lines = code.splitlines()
    changed = False
    # Collect all assignment nodes to modify
    assign_nodes = [
        (i, node)
        for i, node in enumerate(tree.body)
        if isinstance(node, ast.Assign)
        and any(isinstance(target, ast.Name) and target.id == var_name for target in node.targets)
    ]

    # If nothing to change, return unmodified code
    if not assign_nodes:
        return code

    # Perform replacements for all matching assignments (from last to first to not break line offsets)
    for i, node in reversed(assign_nodes):
        start_line = node.lineno - 1
        line = lines[start_line]
        indent = ' ' * (len(line) - len(line.lstrip()))
        lines[start_line] = f"{indent}{var_name} = {value}"
        next_line = len(lines)
        for next_node in tree.body[i+1:]:
            if hasattr(next_node, 'lineno'):
                next_line = next_node.lineno - 1
                break
        if next_line > start_line + 1:
            lines[start_line+1:next_line] = []
        changed = True

    return '\\n'.join(lines) if changed else code

if __name__ == "__main__":
    unittest.main()


test_main.py

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Challenge: Damped Oscillator Simulation

Solution

Challenge: Damped Oscillator Simulation

Solution