Lesson 8, Topic 2
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Vertical Oscillations of a Spring Mass System

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Topic Content:

• Dimensions of Physical Quantities

Let’s say we have rigid support and a string hanging from the support. Let’s say we then attach a mass, there will be a small elongation, e, in the spring.

At this point the spring-mass system is in equilibrium, therefore, all the forces acting will cancel out each other, i.e the net force = 0.

Fnet = 0

The two forces are the restoring force acting upwards and mg acting downwards and their net force is zero.

âˆ´ F + mg = 0

F = -mg

We know F = –ke

ke + mg = 0

âˆ´ –ke = -mg

âˆ´ ke = mg ………. *

From the equilibrium position, if a downward force is applied, the attached mass will be displaced vertically through a distance of x and the system will oscillate with an acceleration, a.

Restoring force, F’ = -k(e + x) ……..(1)

The net force towards centre = Fnet

Fnet = F’ + mg

Fnet = -k(e + x) + mg …..(2)

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