Math & Numbers
Calculate the critical (resonance) speed of a rotating shaft using the single-DOF rotor model. ω_n = √(k/m), n_cr = (60/2π)·√(k/m) rpm. Also returns the natural frequency f_n in Hz.
Call this tool from your code in three languages.
curl -X POST 'https://api.elysiatools.com/en/api/tools/shaft-critical-speed' \
-H 'Content-Type: application/json' \
-d '{"stiffness":200000,"mass":5,"decimalPlaces":4}'Send a POST request with your inputs as JSON. File parameters require a separate upload first.
POST https://api.elysiatools.com/en/api/tools/shaft-critical-speed| Name | Type | Required | Description |
|---|---|---|---|
| stiffness | number | Yes | — |
| mass | number | Yes | — |
| decimalPlaces | number | No | — |
JSON result
{
"key": {...},
"metadata": {
"key": "value"
},
"error": "Error message (optional)",
"message": "Notification message (optional)"
}Add this tool to your Model Context Protocol server so AI agents can list and call it.
Add this block to your MCP client configuration:
{
"mcpServers": {
"elysiatools-shaft-critical-speed": {
"name": "shaft-critical-speed",
"description": "Calculate the critical (resonance) speed of a rotating shaft using the single-DOF rotor model. ω_n = √(k/m), n_cr = (60/2π)·√(k/m) rpm. Also returns the natural frequency f_n in Hz.",
"baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=shaft-critical-speed",
"command": "",
"args": [],
"env": {},
"isActive": true,
"type": "sse"
}
}
}After connecting to the SSE endpoint, list the exposed tools:
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Invoke the tool by its id, passing arguments built from its parameters:
{
"jsonrpc": "2.0",
"id": 2,
"method": "tools/call",
"params": {
"name": "shaft-critical-speed",
"arguments": {
"stiffness": 200000,
"mass": 5,
"decimalPlaces": 4
}
}
}Questions or issues? Contact [email protected]