Q3CQ - College Physics (Urone)

Question

(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?

Step-by-Step Solution

Answer

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

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

Step 1: Definition of frequency

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.

Step 2: (a) Description of Frequency

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.

Step 3: (b) Relation of amplitude and frequency

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.