Answer:
Explanation:
Under the condition where the two simple harmonic motions have the same frequency and a phase difference of either 0 or 180 degrees, their addition will produce a resultant motion that is also a simple harmonic motion. When two simple harmonic motions have the same frequency, it means that they complete their cycles in the same amount of time. This is important because the resulting motion will also have the same frequency. For example, if one motion completes a cycle in 1 second, and the other completes a cycle in the same 1 second, then the resulting motion will also complete a cycle in 1 second. The phase difference between the two motions is crucial in determining whether the resultant is a simple harmonic motion or not. The phase difference refers to the time shift between the two motions. If the phase difference is 0 or 180 degrees, the motions will be in phase or in opposite phase, respectively. When the motions are in phase, their peaks and troughs align, resulting in a larger amplitude. For example, if the two motions have an amplitude of 1 unit, when added together, their amplitudes will add up, resulting in a larger amplitude of 2 units. On the other hand, when the motions are in opposite phase, their peaks and troughs cancel each other out, resulting in a smaller or zero amplitude. For example, if one motion has an amplitude of 1 unit and the other has an amplitude of -1 unit, when added together, their amplitudes will cancel out, resulting in a zero amplitude. In summary, when two simple harmonic motions have the same frequency and a phase difference of 0 or 180 degrees, their addition will produce a resultant motion that is also a simple harmonic motion. The resulting motion will have the same frequency as the individual motions and its amplitude will depend on the phase difference between the two motions.
