Qualitative/quantitative translation (QQT)

Two springs in series or in parallel

Units 2 and 7
8 points
About 18 minutes

You can use a calculator on this question, just like on exam day.

A shorter multipart problem that connects reasoning in words with an equation. You make and justify a claim without equations, derive an equation from a physics principle, and then explain whether the two agree or use them to predict what happens in a changed situation. On the exam: Question 4 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 15–20 minutes. This question type started in May 2025, so Physics C: Mechanics free-response questions from 2024 and earlier are built differently.

The question

A block of mass m rests on a horizontal, frictionless surface and is connected to a wall by two identical light springs, each of spring constant k. In Arrangement 1, the two springs are side by side: each spring connects the block directly to the wall. In Arrangement 2, the springs are connected end to end in a single line between the block and the wall. In each arrangement the block is pulled a small distance from equilibrium and released, so it oscillates.

Suggested time: 18 minutes

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Part (a)

3 points

In which arrangement is the period of oscillation longer, or are the periods equal? Justify your answer without using equations.

Your answer to part (a)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (b)

3 points

Derive expressions for the period of oscillation $T_1$ in Arrangement 1 and $T_2$ in Arrangement 2, in terms of m and k.

Your answer to part (b)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (c)

2 points

Explain how your expressions from part (b) support your answer to part (a). Then use them to predict what happens to $T_2$ if the block in Arrangement 2 is pulled twice as far from equilibrium before it is released.

Your answer to part (c)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

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