Pendulum Simulation App

summary

An interactive visual simulator of a simple pendulum.

prompt

Create a visual simulator of a simple pendulum that swings back and forth. The app should be in English and feature a user-friendly interface. 

## Layout
- A canvas area to visually display the pendulum swinging.
- A form section with sliders that allow users to adjust the pendulum's length (0.1 to 5 meters), the initial angle (0 to 90 degrees), and gravitational acceleration (0 to 15 m/s²).
- A graph area to display the pendulum's angular displacement over time.

## Interaction
- Users should be able to start and pause the pendulum's motion.
- Sliders should dynamically adjust the parameters of the pendulum, with updates reflected immediately in the simulation.

## Animation
- The pendulum should realistically animate its swinging motion, based on real physics calculations.
- The duration and speed of the animation should be determined by pendulum parameters, providing a natural real-time feel.

## Graph
- Display the angular displacement as a line graph over time.
- Ensure the graph updates in real-time as the simulation progresses.
- Style the graph clearly with axis labels and a grid for better readability.

## Best Practices
- Use smooth transitions for visual updates to enhance user experience.
- Maintain an intuitive user interface to allow for easy manipulation of the pendulum parameters.
- Optimize performance to handle physics calculations and animations efficiently.

original prompt

Build a visual simulator of a simple pendulum swinging back and forth. Add a form with sliders for pendulum length (0.1–5 meters), initial angle (0–90 degrees), and gravitational acceleration (0–15 m/s²). Animate the pendulum’s motion and show a graph of its angular displacement over time.

Q: How should the pendulum be represented visually?
A: yes

Q: What should be the duration and speed of the animation?
A: yes

Q: What kind of graph style do you prefer for angular displacement?
A: decide

generation cost summary

model name: claude-3-7-sonnet-latest

response time: 74.58 sec.

result tokens: 6,442

cost: $0.09887700