Adding DampedOscillator code (#6801)

* Adding DampedOscillator code

* Adding one more test case

* Adding one more test case

* Adding one more test case

* Fixing build issues.

* Fixing build issues.

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

@@ -0,0 +1,143 @@
+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)");
+    }
+}