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An object oscillates with simple harmonic motion - Edexcel - A-Level Physics - Question 9 - 2023 - Paper 2
Question 9
An object oscillates with simple harmonic motion. The object has kinetic energy $E_k$ and displacement $x$. Which of the following graphs shows the variation of $E_... show full transcript
Worked Solution & Example Answer:An object oscillates with simple harmonic motion - Edexcel - A-Level Physics - Question 9 - 2023 - Paper 2
Step 1
Identify Kinetic Energy in Simple Harmonic Motion
Answer
In simple harmonic motion (SHM), the kinetic energy of an object varies with its displacement from the equilibrium position. The kinetic energy () can be expressed as:
E_k = rac{1}{2} k (A^2 - x^2)
where:
- is the spring constant,
- is the amplitude of the motion,
- is the displacement.
From this expression, it can be seen that as displacement increases towards the amplitude , the kinetic energy decreases to zero at maximum displacement.
Step 2
Analyze Graphs for Variation of Kinetic Energy
Answer
Looking at the nature of the kinetic energy expression in SHM, we know that it forms a parabola. As approaches , approaches zero. The correct graph will show decreasing quadratically as approaches the amplitude, indicating that the kinetic energy at maximum displacement is zero.
Among the provided graphs, Graph B represents this parabolic behavior where the kinetic energy decreases as displacement increases.
Step 3