Read Springs: Shift the Equilibrium Before Timing Motion
A sudden force reversal creates oscillation about a new equilibrium. First find that equilibrium; maximum extension follows from the initial displacement relative to it.
Motion and force questions become simpler when direction, starting condition, time and the acting forces are marked first.
Start with the condition
With initial compression xi under force F, the spring constant is F/xi. Reverse and double the force, locate the new equilibrium, then conserve spring energy about that point.
Build the governing relation
The amplitude is measured from the new equilibrium, not from the natural length or the original compressed position.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
OlympIQ exam lens
- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Treating the final extension as a static response to 2F ignores the energy stored before the force reversal.
Ready to try the pattern?
100% coverage across the linked question.
Practise the linked question