A man weighing $60\,\mathrm{kg}$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\,\mathrm{m}$ and frequency $\frac{2}{\pi}\,\mathrm{Hz}$. Which of the following statement is correct 

For vertical $\mathrm{SHM}$, the apparent weight is the normal reaction $N$. $$N = m(g+a)$$ In $\mathrm{SHM}$, maximum acceleration is $$a_{\max} = \omega^2 A$$ The angular frequency is $$\omega = 2\pi f = 2\pi \times \frac{2}{\pi} = 4\,\mathrm{rad\,s^{-1}}$$ So, $$a_{\max} = 4^2 \times 0.1 = 1.6\,\mathrm{m\,s^{-2}}$$ Hence the reaction fluctuates between $$N_{\min} = m(g-a_{\max})$$ and $$N_{\max} = m(g+a_{\max})$$ For $m=60\,\mathrm{kg}$, $$N_{\min} = 60(9.8-1.6) = 492\,\mathrm{N}$$ $$N_{\max} = 60(9.8+1.6) = 684\,\mathrm{N}$$ A spring balance calibrated in $\mathrm{kg}$ shows $\frac{N}{g}$. Therefore the reading varies between $$\frac{492}{9.8} \approx 50.2\,\mathrm{kg}$$ and $$\frac{684}{9.8} \approx 69.8\,\mathrm{kg}$$ So the reading fluctuates between $50\,\mathrm{kg}$ and $70\,\mathrm{kg}$. After checking the options, this matches option $D$.