Adding DampedOscillator code

src/main/java/com/thealgorithms/physics/DampedOscillator.java

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+package com.thealgorithms.physics;
+
+/**
+ * Models a damped harmonic oscillator, capturing the behavior of a mass-spring-damper system.
+ *
+ * <p>The system is defined by the second-order differential equation:
+ *     x'' + 2 * gamma * x' + omega₀² * x = 0
+ * where:
+ * <ul>
+ *   <li><b>omega₀</b> is the natural (undamped) angular frequency in radians per second.</li>
+ *   <li><b>gamma</b> is the damping coefficient in inverse seconds.</li>
+ * </ul>
+ *
+ * <p>This implementation provides:
+ * <ul>
+ *   <li>An analytical solution for the underdamped case (γ < ω₀).</li>
+ *   <li>A numerical integrator based on the explicit Euler method for simulation purposes.</li>
+ * </ul>
+ *
+ * <p><strong>Usage Example:</strong>
+ * <pre>{@code
+ * DampedOscillator oscillator = new DampedOscillator(10.0, 0.5);
+ * double displacement = oscillator.displacementAnalytical(1.0, 0.0, 0.1);
+ * double[] nextState = oscillator.stepEuler(new double[]{1.0, 0.0}, 0.001);
+ * }</pre>
+ *
+ * @author [Yash Rajput](https://github.com/the-yash-rajput)
+ */
+public final class DampedOscillator {
+
+    /** Natural (undamped) angular frequency (rad/s). */
+    private final double omega0;
+
+    /** Damping coefficient (s⁻¹). */
+    private final double gamma;
+
+    private DampedOscillator() {
+        throw new AssertionError("No instances.");
+    }
+
+    /**
+     * Constructs a damped oscillator model.
+     *
+     * @param omega0 the natural frequency (rad/s), must be positive
+     * @param gamma  the damping coefficient (s⁻¹), must be non-negative
+     * @throws IllegalArgumentException if parameters are invalid
+     */
+    public DampedOscillator(double omega0, double gamma) {
+        if (omega0 <= 0) {
+            throw new IllegalArgumentException("Natural frequency must be positive.");
+        }
+        if (gamma < 0) {
+            throw new IllegalArgumentException("Damping coefficient must be non-negative.");
+        }
+        this.omega0 = omega0;
+        this.gamma = gamma;
+    }
+
+    /**
+     * Computes the analytical displacement of an underdamped oscillator.
+     * Formula: x(t) = A * exp(-γt) * cos(ω_d t + φ)
+     *
+     * @param amplitude the initial amplitude A
+     * @param phase     the initial phase φ (radians)
+     * @param time      the time t (seconds)
+     * @return the displacement x(t)
+     */
+    public double displacementAnalytical(double amplitude, double phase, double time) {
+        double omegaD = Math.sqrt(Math.max(0.0, omega0 * omega0 - gamma * gamma));
+        return amplitude * Math.exp(-gamma * time) * Math.cos(omegaD * time + phase);
+    }
+
+    /**
+     * Performs a single integration step using the explicit Euler method.
+     * State vector format: [x, v], where v = dx/dt.
+     *
+     * @param state the current state [x, v]
+     * @param dt    the time step (seconds)
+     * @return the next state [x_next, v_next]
+     * @throws IllegalArgumentException if the state array is invalid or dt is non-positive
+     */
+    public double[] stepEuler(double[] state, double dt) {
+        if (state == null || state.length != 2) {
+            throw new IllegalArgumentException("State must be a non-null array of length 2.");
+        }
+        if (dt <= 0) {
+            throw new IllegalArgumentException("Time step must be positive.");
+        }
+
+        double x = state[0];
+        double v = state[1];
+        double acceleration = -2.0 * gamma * v - omega0 * omega0 * x;
+
+        double xNext = x + dt * v;
+        double vNext = v + dt * acceleration;
+
+        return new double[] {xNext, vNext};
+    }
+
+    /** @return the natural (undamped) angular frequency (rad/s). */
+    public double getOmega0() {
+        return omega0;
+    }
+
+    /** @return the damping coefficient (s⁻¹). */
+    public double getGamma() {
+        return gamma;
+    }
+}

src/test/java/com/thealgorithms/physics/DampedOscillatorTest.java

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+package com.thealgorithms.physics;
+
+import static org.junit.jupiter.api.Assertions.assertAll;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for {@link DampedOscillator}.
+ *
+ * <p>Tests focus on:
+ * <ul>
+ *   <li>Constructor validation</li>
+ *   <li>Analytical displacement for underdamped and overdamped parameterizations</li>
+ *   <li>Basic numeric integration sanity using explicit Euler for small step sizes</li>
+ *   <li>Method argument validation (null/invalid inputs)</li>
+ * </ul>
+ */
+@DisplayName("DampedOscillator — unit tests")
+public class DampedOscillatorTest {
+
+    private static final double TOLERANCE = 1e-3;
+
+    @Test
+    @DisplayName("Constructor rejects invalid parameters")
+    void constructorValidation() {
+        assertAll("invalid-constructor-params",
+            ()
+                -> assertThrows(IllegalArgumentException.class, () -> new DampedOscillator(0.0, 0.1), "omega0 == 0 should throw"),
+            () -> assertThrows(IllegalArgumentException.class, () -> new DampedOscillator(-1.0, 0.1), "negative omega0 should throw"), () -> assertThrows(IllegalArgumentException.class, () -> new DampedOscillator(1.0, -0.1), "negative gamma should throw"));
+    }
+
+    @Test
+    @DisplayName("Analytical displacement matches expected formula for underdamped case")
+    void analyticalUnderdamped() {
+        double omega0 = 10.0;
+        double gamma = 0.5;
+        DampedOscillator d = new DampedOscillator(omega0, gamma);
+
+        double a = 1.0;
+        double phi = 0.2;
+        double t = 0.123;
+
+        // expected: a * exp(-gamma * t) * cos(omega_d * t + phi)
+        double omegaD = Math.sqrt(Math.max(0.0, omega0 * omega0 - gamma * gamma));
+        double expected = a * Math.exp(-gamma * t) * Math.cos(omegaD * t + phi);
+
+        double actual = d.displacementAnalytical(a, phi, t);
+        assertEquals(expected, actual, 1e-12, "Analytical underdamped displacement should match closed-form value");
+    }
+
+    @Test
+    @DisplayName("Analytical displacement gracefully handles overdamped parameters (omegaD -> 0)")
+    void analyticalOverdamped() {
+        double omega0 = 1.0;
+        double gamma = 2.0; // gamma > omega0 => omega_d = 0 in our implementation (Math.max)
+        DampedOscillator d = new DampedOscillator(omega0, gamma);
+
+        double a = 2.0;
+        double phi = Math.PI / 4.0;
+        double t = 0.5;
+
+        // With omegaD forced to 0 by implementation, expected simplifies to:
+        double expected = a * Math.exp(-gamma * t) * Math.cos(phi);
+        double actual = d.displacementAnalytical(a, phi, t);
+
+        assertEquals(expected, actual, 1e-12, "Overdamped handling should reduce to exponential * cos(phase)");
+    }
+
+    @Test
+    @DisplayName("Explicit Euler step approximates analytical solution for small dt over short time")
+    void eulerApproximatesAnalyticalSmallDt() {
+        double omega0 = 10.0;
+        double gamma = 0.5;
+        DampedOscillator d = new DampedOscillator(omega0, gamma);
+
+        double a = 1.0;
+        double phi = 0.0;
+
+        // initial conditions consistent with amplitude a and zero phase:
+        // x(0) = a, v(0) = -a * gamma * cos(phi) + a * omegaD * sin(phi)
+        double omegaD = Math.sqrt(Math.max(0.0, omega0 * omega0 - gamma * gamma));
+        double x0 = a * Math.cos(phi);
+        double v0 = -a * gamma * Math.cos(phi) - a * omegaD * Math.sin(phi); // small general form
+
+        double dt = 1e-4;
+        int steps = 1000; // simulate to t = 0.1s
+        double tFinal = steps * dt;
+
+        double[] state = new double[] {x0, v0};
+        for (int i = 0; i < steps; i++) {
+            state = d.stepEuler(state, dt);
+        }
+
+        double analyticAtT = d.displacementAnalytical(a, phi, tFinal);
+        double numericAtT = state[0];
+
+        // Euler is low-order — allow a small tolerance but assert it remains close for small dt + short time.
+        assertEquals(analyticAtT, numericAtT, TOLERANCE, String.format("Numeric Euler should approximate analytical solution at t=%.6f (tolerance=%g)", tFinal, TOLERANCE));
+    }
+
+    @Test
+    @DisplayName("stepEuler validates inputs and throws on null/invalid dt/state")
+    void eulerInputValidation() {
+        DampedOscillator d = new DampedOscillator(5.0, 0.1);
+
+        assertAll("invalid-stepEuler-args",
+            ()
+                -> assertThrows(IllegalArgumentException.class, () -> d.stepEuler(null, 0.01), "null state should throw"),
+            ()
+                -> assertThrows(IllegalArgumentException.class, () -> d.stepEuler(new double[] {1.0}, 0.01), "state array with invalid length should throw"),
+            () -> assertThrows(IllegalArgumentException.class, () -> d.stepEuler(new double[] {1.0, 0.0}, 0.0), "non-positive dt should throw"), () -> assertThrows(IllegalArgumentException.class, () -> d.stepEuler(new double[] {1.0, 0.0}, -1e-3), "negative dt should throw"));
+    }
+
+    @Test
+    @DisplayName("Getter methods return configured parameters")
+    void gettersReturnConfiguration() {
+        double omega0 = Math.PI;
+        double gamma = 0.01;
+        DampedOscillator d = new DampedOscillator(omega0, gamma);
+
+        assertAll("getters", () -> assertEquals(omega0, d.getOmega0(), 0.0, "getOmega0 should return configured omega0"), () -> assertEquals(gamma, d.getGamma(), 0.0, "getGamma should return configured gamma"));
+    }
+
+    @Test
+    @DisplayName("Analytical displacement at t=0 returns initial amplitude * cos(phase)")
+    void analyticalAtZeroTime() {
+        double omega0 = 5.0;
+        double gamma = 0.2;
+        DampedOscillator d = new DampedOscillator(omega0, gamma);
+
+        double a = 2.0;
+        double phi = Math.PI / 3.0;
+        double t = 0.0;
+
+        double expected = a * Math.cos(phi);
+        double actual = d.displacementAnalytical(a, phi, t);
+
+        assertEquals(expected, actual, 1e-12, "Displacement at t=0 should be a * cos(phase)");
+    }
+}