Oscillations and Radiation Problem Solving

This final lesson brings together all the material from the course into exam-style problem solving. We will work through the types of calculations and analysis questions that regularly appear in Edexcel A-Level Physics papers on oscillations and nuclear radiation. The focus is on selecting the right equation, interpreting graphs, and combining concepts.

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SHM Calculation Strategy

When faced with an SHM problem, follow this approach:

1. Identify what you know: amplitude A, frequency f or period T, mass m, spring constant k, displacement x, velocity v, or acceleration a
2. Calculate ω if not given: ω = 2πf = 2π/T, or ω = √(k/m), or ω = √(g/L)
3. Choose the right equation based on what you need to find:
   • Displacement: x = A cos(ωt) or x = A sin(ωt)
   • Velocity from time: v = −Aω sin(ωt) or v = Aω cos(ωt)
   • Velocity from displacement: v = ±ω√(A² − x²)
   • Acceleration: a = −ω²x
   • Maximum values: v_max = Aω, a_max = Aω²
   • Energy: KE = ½mω²(A² − x²), PE = ½mω²x², E_total = ½mω²A²

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Worked Example 1: SHM Amplitude and Speed