Read before you solve · 3 min
Read Potential Curves: Differentiate Before You Judge
A conservative force is minus the slope of potential energy. Equilibrium points are stationary points of U, and their curvature determines whether they are stable.
NSEP · Mechanics · 1 linked question · 100% coverage
Know this first
Motion and force questions become simpler when direction, starting condition, time and the acting forces are marked first.
Distance · Length of the path travelledDisplacement · Straight-line change in positionResultant force · Net force including direction
Study deeper: NCERT Physics · Mechanics
Start with the condition
Calculate F = -dU/dx
Solve dU/ dx = 0, then use d² U/dx-squared: positive means a local minimum and stable equilibrium;
negative means unstable.
Build the governing relation
For small oscillations about a stable x-zero, use ω
squared = U-double-prime(x-zero)/m
Units of U-double-prime/m must be s to the minus two.
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.
OlympIQ trap
A point where U is zero is not automatically an equilibrium; only zero slope gives zero force.
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