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Example: A mass of 0.5 kg is attached to a spring with a spring constant of 20 N/m. The mass is pulled 0.1 m from its rest position and released from rest (phase φ=0). Find the displacement, velocity, and acceleration of the mass at time t = 1 s. Step 1: Find angular frequency ω = √(k/m) = √(20 / 0.5) = √40 ≈ 6.32 rad/s. Step 2: Amplitude A = 0.1 m, phase φ = 0. Step 3: Displacement x(t) = A cos(ωt + φ) = 0.1 cos(6.32 * 1) ≈ 0.1 cos(6.32) ≈ 0.1 * 0.99 ≈ 0.099 m. Step 4: Velocity v(t) = -A ω sin(ωt + φ) = -0.1 * 6.32 * sin(6.32) ≈ -0.632 * 0.14 ≈ -0.088 m/s. Step 5: Acceleration a(t) = -A ω² cos(ωt + φ) = -0.1 * (6.32)² * cos(6.32) ≈ -0.1 * 39.94 * 0.99 ≈ -3.95 m/s². So at t = 1 s: displacement ≈ 0.099 m to the right, velocity ≈ -0.088 m/s (moving left), acceleration ≈ -3.95 m/s² (toward the rest position).