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For JEE SHM problems, follow a systematic approach. Step 1: Identify the restoring force. Displace the system by $x$ from equilibrium and compute the net force. If $F = -kx$, it is SHM with $\omega = \sqrt{k/m}$. Step 2: For complex systems (pulleys, levers, floating bodies), use the energy method. Write total energy $E = \frac{1}{2}m_{\text{eff}}\dot{x}^2 + \frac{1}{2}k_{\text{eff}}x^2$ and extract $T = 2\pi\sqrt{m_{\text{eff}}/k_{\text{eff}}}$.

Step 3: For velocity/acceleration at a position, use $v = \omega\sqrt{A^2-x^2}$ and $a = -\omega^2 x$ directly. Step 4: For energy partition, use $KE/E = 1-x^2/A^2$ and $PE/E = x^2/A^2$. Step 5: For time calculations, use the reference circle method.

Common traps to avoid: (1) Using pendulum formula for spring systems or vice versa. (2) Forgetting that cutting a spring changes $k$. (3) Not replacing $g$ with $g_{\text{eff}}$ in non-inertial frames (for pendulums). (4) Confusing KE = PE position ($A/\sqrt{2}$) with KE = 3PE position ($A/2$). (5) Assuming time is proportional to distance in SHM. Always verify dimensions of your answer and check limiting cases.