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: