Simple Harmonic Motion for a Horizontally Stretched String

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The tension in a stretched string is usually expressed in terms of it’s modulus of elasticity4b42b39e.gif” name=”Object1″ align=”ABSMIDDLE” width=”80″ height=”40″ hspace=”8″>This is in fact an expression of Hooke’s Law – Force is proportional to extension.

Suppose that a string of length l is stretched between two points A and B. A particle P is attached to the string at C between the points A and B.

Suppose the lengths AC and CB are in the ratiothen the natural length of AC is and the extension of AC isSimilarly the natural length of CB is and the extension of CB is

Suppose the particle P is pulled an extra distance x to the right.

The extension of AC is now so

Similarly

It will experience a net force to the left, towards the equilibrium position C of magnitude

Now applywith which has the form of simple harmonic motionwith

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