Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain why SHM is a special case of periodic motion, and give a periodic motion that is not SHM. (Guide: “Periodic motion and SHM”; Practice Q7)
- I can define an equilibrium position as a place of zero net force, and a restoring force as one opposite to the displacement. (Guide: Figure 1)
- I can state the SHM condition m a_x = −kΔx (or F_net = −kx with x measured from equilibrium) and explain what both the minus sign and the proportionality mean. (Guide: “The condition for SHM”; Practice Q1)
- I can explain why a constant force such as gravity shifts the equilibrium but does not stop the motion being SHM. (Guide: Worked example 2; Practice Q5(d))
Skills
- I can find an equilibrium position from a force law or from U(x), and measure displacement from it. (Guide: Worked example 1; Practice Q3)
- I can use F_net = −kx and Newton’s second law to find an acceleration with the correct sign and units. (Practice Q2)
- I can extract k and the equilibrium position from force–position data. (Practice Q4)
- I can derive d²u/dt² = −(k/m)u for a block on a vertical spring. (Guide: Worked example 2; Practice Q5)
- I can find k_eff = d²U/dx² for small oscillations about a stable minimum of U(x). (Guide: Worked example 3; Practice Q6)
Reasoning
- I can decide whether a force law gives SHM, other periodic motion, or no oscillation at all. (Guide: Worked example 1)
- I can judge how accurate the SHM model is at a given displacement by comparing the exact force with −k_eff u. (Guide: Figure 2; Practice Q6(d))
- I can explain why a small-angle pendulum is close to SHM and why the angle must be in radians. (Guide: “The pendulum: SHM in an angle”)
All ticked? Move on to Topic 7.2, Frequency and Period of SHM, or return to the course roadmap.