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The graph shows the variation of displacement $d$ with time $t$ for a particle moving with simple harmonic motion of period $T$ - AQA - A-Level Physics - Question 29 - 2019 - Paper 1
Question 29
The graph shows the variation of displacement $d$ with time $t$ for a particle moving with simple harmonic motion of period $T$. Which graph shows the variation of ... show full transcript
Worked Solution & Example Answer:The graph shows the variation of displacement $d$ with time $t$ for a particle moving with simple harmonic motion of period $T$ - AQA - A-Level Physics - Question 29 - 2019 - Paper 1
Step 1
Which graph shows the variation of kinetic energy $\overline{E_k}$ of the particle with time?
Answer
In simple harmonic motion, the kinetic energy of a particle varies with time as it moves through its displacement. The kinetic energy is maximum when the displacement is zero (i.e., when the particle is at the equilibrium position) and minimum when the displacement is maximum (at the amplitude).
Given that the displacement graph is a sinusoidal wave, the kinetic energy variation over one complete period would display similar periodic behavior:
- At and , the displacement is zero and thus the kinetic energy is at its maximum.
- At and , the displacement is at its maximum and therefore the kinetic energy is at its minimum.
This periodic behavior means that the graph of kinetic energy will resemble the shape of the square of the sine function, peaking when the displacement is at zero. Therefore, the correct graph that represents this behavior is option B.