A body of mass m is hanging from a wire of length l. It is pulled by a distance Δl and left. It executes simple harmonic motion. If the young’s modulus of the wire is Y, area of $$cross-section$$ is A, then the frequency of oscillation is

Question

A body of mass m is hanging from a wire of length l. It is pulled by a distance  Δl  and left. It executes simple harmonic motion. If the young’s modulus of the wire is  Y, area of $$cross-section$$ is A, then the frequency of oscillation is

Infinity Learn · Accepted Answer

For a body under stress we know that its Young’s modulus can be written as   $$Y=FlA$$Δl. Here  FA is stress and Δll is strain. This restoring force can be also  written as $$F=$$−kΔl . Hence, we get $$k=F$$Δ$$l=YAl$$. We know that for a simple harmonic  motion the frequency of oscillation is given by  $$f=12$$$$π$$km . Substituting for the  value of  k we get  $$f=12$$$$π$$YAml.

A body of mass m is hanging from a wire of length l. It is pulled by a distance $Δ l$ and left. It executes simple harmonic motion. If the young’s modulus of the wire is Y, area of cross-section is A, then the frequency of oscillation is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A body of mass m is hanging from a wire of length l. It is pulled by a distance Δl and left. It executes simple harmonic motion. If the young’s modulus of the wire is Y, area of cross-section is A, then the frequency of oscillation is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A body of mass m is hanging from a wire of length l. It is pulled by a distance $Δ l$ and left. It executes simple harmonic motion. If the young’s modulus of the wire is Y, area of cross-section is A, then the frequency of oscillation is