Q.
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 π2Hz. Which of the following statement is correct?
The maximum force acting on the body executing simple harmonic motion is mω2a=m×(2πf)2a=60×(2π×π2)2×0.1N =60×16×0.1=96N=9.896≈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 50kgf and 70kgf.