At a turning point, the kinetic ledger is zero. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

At the turning point, velocity is zero

The position equals the amplitude, so all 16 joules are in the spring ledger.

x=A=4 mU=16 Jx=A=4\ \mathrm{m}\Rightarrow U=16\ \mathrm{J}
Turning point ledgerThe spring energy equals the total energy.k=2 N/mA=4 mx=4 mE=16 JU=16 JK=0 J

Kinetic energy is zero at the endpoint

The checked kinetic entry is 0, not an inferred caption.

K=0K=0
Endpoint kinetic ledgerThe energy check enforces K plus U equals E.k=2 N/mA=4 mx=4 mE=16 JU=16 JK=0 J