Physics Study Guide/Periodic Motion

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Springs[edit]

Hooke's law[edit]

\vec{F}=-k\vec{x}

k is the spring constant and x is the displacement (the force is the restoring force)

For this equation to be approximately accurate, x needs to be below the spring's elastic limit. If x is more than the spring's elastic limit, the spring will exhibit "plastic behaviour" meaning that it will not return to its original position.

Potential energy[edit]

potential energy stored in a compressed recoiled spring

U= -\int\limits_{0}^{x_f} -k\vec{x}\cdot\vec{\mathrm{d}x} = \frac{1}{2} kx_f^2


T is the period, m is the mass, and k is the spring constant.

T=2 \pi \sqrt{{m \over k}}