Step 1: Identify the restoring force and verify it is proportional to displacement. Step 2: Find $\omega$ from $F = -m\omega^2 x$ (compare with $F = -kx$ to get $\omega = \sqrt{k/m}$). Step 3: Determine $A$ and $\phi$ from initial conditions ($x_0$ and $v_0$ at $t = 0$). Step 4: Write the complete equation $x = A\sin(\omega t + \phi)$. Step 5: Extract the required quantity (velocity, acceleration, energy, time). For energy problems, often the direct formula $v = \omega\sqrt{A^2 - x^2}$ is faster than differentiating the displacement equation.