AP Physics 1 · Summary

Unit 7 summary

1. Simple harmonic motion needs a restoring force proportional to the displacement and opposite to it: $F = -kx$, so $a = -\frac{k}{m}x$.
2. At a turning point the speed is zero and the restoring force and acceleration are largest; at equilibrium the speed is largest and the restoring force is zero.
3. $f = 1/T$. A mass on a spring has $T = 2\pi\sqrt{m/k}$; a pendulum at small angles has $T = 2\pi\sqrt{L/g}$.
4. The amplitude does not change either period (for a pendulum, while the angle stays small); the bob’s mass does not change a pendulum’s period, and g does not change a spring’s.
5. Total energy is $\frac{1}{2}kA^2$, and $\frac{1}{2}kx^2 + \frac{1}{2}mv^2$ stays equal to it, so $v_{max} = A\sqrt{k/m}$.
6. Energy goes as the amplitude squared: double the amplitude and you get four times the energy and twice the maximum speed, with the same period.
7. In an experiment, change one variable at a time, time many cycles and divide, and compare the results with what the model predicts.