Damped, Forced Oscillations & Superposition question from JEE Main 2013 (23 Apr, Shift 1)

Answer: (d)

1. The DC coil acts as a magnet and pulls the iron bob down, so the effective $g$ increases.
2. $T = 2\pi\sqrt{l/g_{\text{eff}}}$ with $g_{\text{eff}} > g \Rightarrow T < 2\pi\sqrt{l/g}$.
3. The moving iron bob in the coil's non-uniform field has eddy currents, which oppose motion, so damping is larger than in air alone.
4. So the answer is (d).