Translation between representations (TBR)
Block on a horizontal spring: equations and graphs
- Units 2 and 7
- 12 points
- About 28 minutes
You can use a calculator on this question, just like on exam day.
A multipart problem about one situation shown in several ways. You draw a diagram, derive equations, sketch or draw graphs, and then explain whether your answers agree with each other or use them to predict what happens when the situation changes. On the exam: Question 2 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 25–30 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 = 0.40 kg is attached to a horizontal spring of spring constant k = 10 N/m and oscillates on a frictionless surface. The position x of the block is measured from the equilibrium position, with +x to the right. At time t = 0, the block passes through the equilibrium position moving to the left with speed 0.40 m/s.
Suggested time: 28 minutes
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Part (a)
2 pointsStarting from Newton's second law, write a differential equation for the block's position x(t), and determine the angular frequency ω of its motion in terms of k and m.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (b)
3 pointsThe block's motion can be written . Determine the values of A, ω, and φ for this motion, and the period T.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (c)
3 pointsDescribe graphs of the block's position x and velocity v as functions of time from t = 0 to t = T. Include the axes and labels with units, the shape of each graph, and the times and values of the maximums, minimums, and zeros.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (d)
2 pointsDescribe graphs of the block's kinetic energy K and the spring's potential energy U as functions of time from t = 0 to t = T, on the same axes.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (e)
2 pointsExplain how your graphs in parts (c) and (d) are consistent with each other at t = T/4 and at t = T/2.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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