Q. 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 statements is correct
A) The spring balance reads the weight of man as $60\ kg$
B) The spring balance reading fluctuates between $60\ kg$ and $70\ kg$
C) The spring balance reading fluctuates between $50\ kg$ and $60\ kg$
D) The spring balance reading fluctuates between $50\ kg$ and $70\ kg$
Explanation
(d) The maximum force acting on the body executing simple harmonic motion is
$m\omega^{2}a = m \times (2\pi f)^{2}a = 60 \times \left( 2\pi \times \frac{2}{\pi} \right)^{2} \times 0.1N$
$= 60 \times 16 \times 0.1 = 96N = \frac{96}{9.8} \approx 10kgf$ and this force is towards mean position
The reaction of the force on the platform away from the mean position. It reduces the weight of man on upper extreme, $i.e.,$ net weight $= (60 - 10)kgf.$
This force adds to the weight at lower extreme position
$i.e.,$ net weight becomes $= (60 + 10)kgf$
Therefore, the reading the weight recorded by spring balance fluctuates between $50\ kgf$ and $70\ kgf$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.