Question

A man weighing $60kg$ stands on the horizontal platform

of a spring balance. The platform starts executing simple harmonic motion of
amplitude $0.1m$ and frequency $\frac{2}{\pi }$ Hz.

• A. The spring balance reads the weight of man as $60kg$
• B. The spring balance reading fluctuates between $60kg$. and $70kg$
• C. The spring balance reading fluctuates between $50kg$ and $60kg$
• D. The spring balance reading fluctuates between $50kg$ and $70kg$

Answer 1

The correct option is D The spring balance reading fluctuates between $50kg$ and $70kg$

The maximum force acting on the body executing simple harmonic motion is,

$m{\omega }^2=m\times (2\pi f{)}^{2}a=60\times (2\pi \times \frac{2}{\pi }{)}^2\times 0.1N$

$=60\times 16\times 0.1=96N=-\frac{96}{9.8}=10kgf$ and this force is towards mean position.

The reaction on the platform away from the mean position it reduce the weight of men on upper extreme.

That is, Net weight, $=(60-10)kgf$

This force adds to the weight at lower extreme position. That is, net weight become $=(60+10)kgf$

Therefore the reading the weight recording by spring ba;ance fluctes between $50kgf$ and $70kgf$.