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Is the period of a vibrating spring linearly affected by the mass of the attached object?
Wiki User
∙ 13y ago
Let a mass m be attached to the end of a spring with spring constant k. The spring extends and comes to rest with an equilibrium extension e.
At equilibrium; Weight = Force exerted by spring
=> mg = ke -------- 1
Suppose the spring is displaced through a displacement x downwards from its equilibrium position:
Resolving vertically, we have;
Resultant force on mass = Force exerted by spring - Weight of mass
=> ma = k(e + x) - mg ------- 2
From 1, we have:
ma = mg + kx - mg
=> a = (k/m)x
Since a is proportional to displacement from equilibrium position, the oscillation is simple harmonic.
So, (angular velocity)2 = (k/m)
=> 2pi/T = (k/m)1/2
=> T = 2pi (m/k)1/2
This equation shows that the time period is proportional to the square root of the mass of the attached object.
Wiki User
∙ 13y ago
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