A particle of mass is acted on by a force

where and are positive constants, and is the particle’s displacement from the origin.

**Question:** By using the chain rule, show that this equation of motion is exactly equivalent to one of the form

and deduce an equivalence for . How might you describe the two forces at work?

**Extension:** Given that the particle starts from rest at the origin, show that the particle’s position after time is given by

or an equivalent, expressed in terms of .

**Hint: **The chain rule provides the following relation:

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