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Q3CQ

Expert-verifiedFound in: Page 588

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**(a) If the frequency is not constant for some oscillation, can the oscillation be simple harmonic motion?**

**(b) Can you think of any examples of harmonic motion where the frequency may depend on the amplitude?**

(a) The oscillation cannot be simple harmonic if the frequency is not constant.

(b) No, in harmonic oscillation, frequency does not depend on amplitude.

**The expression for the frequency for simple harmonic motion is given as follows,**

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

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

It is known that for the motion to be simple harmonic, it is necessary to have a constant frequency. It is due to the fact that spring constant and mass are both constants in the system, therefore frequency is also constant.

Thus, if frequency is not constant for an oscillation, it cannot be simple harmonic motion.

Consider the formula of frequency.

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

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

Thus, there are no harmonic motions where frequency depends on the amplitude.

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