Question

What is arbitrary motion ?

Answer 1

Hint: Consider all the types of motion and think of arbitrary motion. You can also ponder about the word arbitrary.Arbitrary means random, it means we do not know anything about the path and hence it cannot be calculated or exactly known.

Complete step by step answer:
In the higher studies, you will know that the term arbitrary motion is used to denote growing or decaying oscillations with a certain frequency. It can be understood as just a random direction which is used to just refer to some motion and we are not required to produce anything out of that direction. In such types of questions, in arbitrary motion, it has nothing to do with the direction.

For example, a null vector is defined as a vector with zero magnitude and an arbitrary direction. In this case, we can consider any direction. Similarly for any vector with magnitude 1, we may consider any direction as we are working on the magnitude of the vector not the direction. Hence, we are not required to do anything with the direction.

Note:In such case you can use any direction to proceed the question and analyse the situation. Generally, we take the direction which is most familiar to us, like the x-axis. Keep in mind, in this case do not consider a direction in which you face difficulty while solving the problem. Take the direction which depicts the situation easily and does not make the question complex. When you come across the word arbitrary, understand that the question doesn’t require you to work on the direction but on some other factors.