When mass attached to a spiral spring is set into vertical oscillations, it’s acceleration will have a?
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In other words, a vertical spring-mass system will undergo simple harmonic motion in the vertical direction about the equilibrium position. In general, a spring-mass system will undergo simple harmonic motion if a constant force that is co-linear with the spring force is exerted on the mass (in this case, gravity).
When mass attached to a spiral spring is set into vertical oscillations, its acceleration will have a value equal to the acceleration due to gravity.
Proof:
When the mass held by the spiral spring moves upward, the resultant force acting on is:
T + W= ma, where T= tension of the spiral spring, W= weight of the object, m= mass, and a= vertical acceleration.
And when the mass moves downward, that formula changes to:
W - T= ma
Putting these two expressions together,
T= ma - W and T= W - ma,
ma - W= W - ma
ma + ma= W + W
2ma= 2W
Recall, W= mg
2ma= 2mg
a= g.
