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Q4CQ

Expert-verifiedFound in: Page 588

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.**

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A mass attached to a spring on a frictionless surface.

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**Simple Harmonic Motion is a kind of periodic motion where the body oscillates to and from about the equilibrium position**** ****such that the maximum displacement of the body on either side is the same.**

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The force acting on the body during motion is always directed toward the center and is proportional to its displacement.

When a mass attached to a spring system oscillate about its equilibrium point, the restoring force exerted upon the spring is measured such that the force F always acts towards the equilibrium point and is expressed as follows,

\(F = - kx\)

Here, K is the spring constant which is related to the stiffness of the spring. A stiff spring would have a high spring constant and is the amount the spring stretches relative to its equilibrium position.

Write the expression for the frequency for the simple harmonic motion.

\(f = \frac{1}{{2\pi }}\sqrt {\left( {\frac{k}{m}} \right)} \)

Here, k is the spring constant and m is the mass of a system.

It is observed that the frequency does not depend on the amplitude of oscillation but on spring constant and mass.

Thus, the frequency is independent of amplitude.

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