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const state = {
m: 1.0,
k: 100,
c: 5.0,
F0: 10,
p: 5.0,
u0: 0.0,
v0: 0.0,
tMax: 10.0,
dt: 0.001
};
function derivatives(t, u, v) {
const u_prime = v;
const v_prime = (state.F0 * Math.sin(state.p * t) - state.c * v - state.k * u) / state.m;
return { u_prime, v_prime };
}
function solve() {
let t = 0;
let u = state.u0;
let v = state.v0;
let maxU = 0;
const steps = Math.ceil(state.tMax / state.dt);
for (let i = 0; i <= steps; i++) {
const k1 = derivatives(t, u, v);
const t2 = t + state.dt / 2;
const u2 = u + k1.u_prime * state.dt / 2;
const v2 = v + k1.v_prime * state.dt / 2;
const k2 = derivatives(t2, u2, v2);
const t3 = t + state.dt / 2;
const u3 = u + k2.u_prime * state.dt / 2;
const v3 = v + k2.v_prime * state.dt / 2;
const k3 = derivatives(t3, u3, v3);
const t4 = t + state.dt;
const u4 = u + k3.u_prime * state.dt;
const v4 = v + k3.v_prime * state.dt;
const k4 = derivatives(t4, u4, v4);
u += (state.dt / 6) * (k1.u_prime + 2 * k2.u_prime + 2 * k3.u_prime + k4.u_prime);
v += (state.dt / 6) * (k1.v_prime + 2 * k2.v_prime + 2 * k3.v_prime + k4.v_prime);
t += state.dt;
if (Math.abs(u) > maxU) maxU = Math.abs(u);
}
return { finalU: u, maxU: maxU };
}
function runTest(name, params) {
Object.assign(state, params);
const res = solve();
console.log(`Test: ${name}`);
console.log(` Params: ${JSON.stringify(params)}`);
console.log(` Result: Max |u| = ${res.maxU.toFixed(5)}, Final u = ${res.finalU.toFixed(5)}`);
return res;
}
console.log("--- Verification Suite ---");
// 1. Zero Values
runTest("Zero Values", { m: 1, k: 100, c: 5, F0: 0, p: 0, u0: 0, v0: 0 });
// 2. Resonance (omega_n = 10)
// Low damping to see large amplitude
runTest("Resonance", { m: 1, k: 100, c: 1, F0: 10, p: 10, u0: 0, v0: 0 });
// 3. Underdamped Free Vibration (zeta = 0.25)
runTest("Underdamped Free", { m: 1, k: 100, c: 5, F0: 0, p: 0, u0: 1, v0: 0 });
// 4. Critically Damped Free Vibration (zeta = 1.0)
// c = 2 * sqrt(1 * 100) = 20
runTest("Critically Damped Free", { m: 1, k: 100, c: 20, F0: 0, p: 0, u0: 1, v0: 0 });
// 5. Overdamped Free Vibration (zeta = 2.0)
// c = 40
runTest("Overdamped Free", { m: 1, k: 100, c: 40, F0: 0, p: 0, u0: 1, v0: 0 });
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