Challenge: Damped Oscillator Simulation
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.
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Implement a function that computes and returns the displacement of a damped oscillator at each time step, given system parameters and initial conditions.
- Use the analytical solution for an underdamped mass-spring-damper system.
- Compute displacement at each time step from
t = 0toduration, incrementing bydt. - The function should accept mass (
m), spring constant (k), damping coefficient (c), initial displacement (x0), initial velocity (v0), total simulation time (duration), and time step (dt) as arguments. - Return a list of displacement values, one for each time step.
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Can you explain what an underdamped system is?
How do you simulate a damped oscillator?
What are some real-world examples of damped oscillators?
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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.
Swipe to start coding
Implement a function that computes and returns the displacement of a damped oscillator at each time step, given system parameters and initial conditions.
- Use the analytical solution for an underdamped mass-spring-damper system.
- Compute displacement at each time step from
t = 0toduration, incrementing bydt. - The function should accept mass (
m), spring constant (k), damping coefficient (c), initial displacement (x0), initial velocity (v0), total simulation time (duration), and time step (dt) as arguments. - Return a list of displacement values, one for each time step.
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