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Grade: upto college level
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.
4 years ago

Answers : (1)

Jitender Pal
askIITians Faculty
365 Points
							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.

4 years ago
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