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 what the amplitude, angular frequency and phase constant in x = A cos(ωt + φ₀) each tell me, and which ones the system fixes. (Guide: “The solution: x = A cos(ωt + φ₀)”)
- I can state where in the cycle displacement, velocity and acceleration are zero and where each is largest. (Guide: “Zeros and extremes” and Figure 1; Practice Q1)
- I can explain why the period of SHM does not depend on the amplitude, and say what does change when A changes. (Guide: “Amplitude does not change the period”; Practice Q5(d))
- I can describe the natural frequency of a system and explain why a sinusoidal driving force at that frequency makes the amplitude grow. (Guide: “Resonance”; Practice Q3, Q7)
Calculation
- I can apply Newton’s second law to a system and reach d²x/dt² = −ω²x, then read off ω. (Guide: “From Newton’s second law to the SHM equation”; Practice Q5(a)–(b))
- I can find A and φ₀ from x₀ and v_x0, choosing the correct quadrant. (Guide: Worked example 1; Practice Q4)
- I can differentiate x(t) to find v_x(t) and a_x(t), and use v_max = Aω and a_max = Aω². (Guide: “Velocity and acceleration by differentiation”; Practice Q2, Q4)
- I can find the speed at any position from |v_x| = ω√(A² − x²). (Practice Q4(b))
- I can find a spring constant from measured period data using k = mω². (Practice Q6(d))
Reasoning with representations
- I can read A, T, φ₀ and v_max from x–t and v_x–t graphs, and integrate or differentiate to get the other graphs. (Guide: Worked example 2 and Figure 3; Practice Q6)
- I can use an a_x–x graph to test for SHM and find ω² from its slope. (Guide: “Reading SHM from graphs”; Practice Q2)
- I can sketch lined-up x, v_x and a_x graphs for a given starting condition. (Practice Q6(c))
- I can explain why a secant estimate of velocity from data differs from the instantaneous value. (Practice Q6(e))
All ticked? Move on to Topic 7.4, Energy of Simple Harmonic Oscillators, or return to the course roadmap.