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A man weighing $60\ kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\ m$ and frequency $\frac{2}{\pi } Hz$. Which of the following staements is correct
The spring balance reads the weight of man as $60\ kg$
The spring balance reading fluctuates between $60\ kg$. and $70\ kg$
The spring balance reading fluctuates between $50\ kg$ and $60\ kg$
The spring balance reading fluctuates between $50\ kg$ and $70\ kg$
Solution
The maximum force acting on the body executing simple harmonic motion is
$\mathrm{m\omega}^{2} \mathrm{a}=\mathrm{m} \times(2 \pi \mathrm{f})^{2} \mathrm{a}=60 \times\left(2 \pi \times \frac{2}{\pi}\right)^{2} \times 0.1 \mathrm{N}$
$=60 \times 16 \times 0.1=96 \mathrm{N}=\frac{96}{9.8} \approx 10 \mathrm{kgf}$ and this
force is towards mean position.
The reaction of the force on the platform away from the mean position. It readuces the weight of man on upper extreme, i.e., net weight $=(60-10) \mathrm{kgf}$
This force adds to the weight at lower extreme position i.e., net weight becomes $=(60+10) \mathrm{kgf}$ Therefore, the reading the weight recorded by spring balance fluctuates between $50$ $kgf$ and $70$ $\mathrm{kgf}$
