Phase Is a Checked State Ledger

Acceleration Points Back Toward Center

The acceleration sign is bound to the displacement sign. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Positive displacement gives negative acceleration

At the right endpoint, position is 4 metres and the acceleration value is negative 4.

x=4 m⇒a=−4x=4\ \mathrm{m}\Rightarrow a=-4
Acceleration at right endpointThe checked acceleration sign is negative.A=4 momega=1 1/sphase=0x=4 mv=0 m/sa=-4 m/s^2

Negative displacement gives positive acceleration

At the left endpoint, position is negative 4 metres and acceleration is positive 4.

x=−4 m⇒a=4x=-4\ \mathrm{m}\Rightarrow a=4
Acceleration at left endpointThe sign changed because the displacement changed sign.A=4 momega=1 1/sphase=1/2x=-4 mv=0 m/sa=4 m/s^2