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A person stands on a bathroom-type scale, which rests on a platform suspended by a large spring. The whole system executes simple harmonic motion in a vertical direction. Describe the variation in scale reading during a period of motion.

A person stands on a bathroom-type scale, which rests on a platform suspended by a large spring. The whole system executes simple harmonic motion in a vertical direction. Describe the variation in scale reading during a period of motion.

Grade:upto college level

1 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago
The particle goes up from the equilibrium position. So the acceleration will be downward and increasing linearly.
So, net weight of the body will be m(g+a). Here, m is the mass of the body, g is the acceleration due to gravity and a is the acceleration of the system.
As the spring force kx balances the force acting on the system ma, therefore acceleration of the system will be,
ma = kx
So, a = kx/m
Thus the net weight as particle goes up from the equilibrium position,
W = m(g+a)
= m(g+kx/m) (Since a = kx/m)
= mg+kx
As particle moves downward, then acceleration will be upward.
So weight will be,
W = m(g-a)
= m(g-kx/m) (Since a = kx/m)
= mg-kx
Thus, the variation in meter reading is shown below by graph.

235-2089_1.PNG

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