3 min readβ’june 18, 2024

π Welcome to the **AP Physics Unit 6 FRQ (Simple Harmonic Motion) Answers**. Have your responses handy as you go through the rubrics to see how you did!

β± Remember, the AP Physics 1 exam has 5 free-response questions, and you will be given 90 minutes to complete the FRQ section. (This means you should **give yourself ~18 minutes** to go through each practice FRQ.)

**Setup**

A group of students must determine the spring constant k of a spring that hangs vertically from a ring stand. The students attach a block to the bottom of the vertical spring, as shown in Figure 1. The students then pull the block-spring system 0.5 m below the systemβs equilibrium position and release the system so that it oscillates. The students record the mass M of the block and the period of oscillation T for several trials, as shown in Table 1.

**Figure 1**

**Table 1**

M (kg) | T (s) |

0.3 | 0.77 |

0.6 | 1.07 |

0.9 | 1.29 |

1.2 | 1.50 |

**Questions with Answers & Rubric**

**Part A**

The students want to determine the spring constant of the spring.

(i) **Indicate** below which quantities could be graphed to determine the spring constant of the spring by using a best-fit line. You may use the remaining columns in the table above, as needed, to record any quantities (including units) that are not already in the table. (1pt)

- 1pt:
**Vertical Axis**: 4 * Ο^2 * m,**Horizontal Axis**: T^2

M (kg) | T (s) | y = 4 * Ο^2 * m | x = T^2 |

0.3 | 0.77 | 11.8 | 0.5 |

0.6 | 1.07 | 23.7 | 1.14 |

0.9 | 1.29 | 35.5 | 1.66 |

1.2 | 1.50 | 47.3 | 2.25 |

- Study Guide: Period of Simple Harmonic Oscillators

(ii) On the grid below, **plot** the appropriate quantities to determine the spring constant of the spring by using a best-fit line. Clearly scale and label all axes, including units as appropriate. (4pts)

(iii) Use the graph above to **estimate** a value for the spring constant of the spring. (2pts)

**Part B**

Another group of students performs a similar experiment in which the same block-spring system from trial 1 oscillates, but in the horizontal direction, as shown in Figure 2. Frictional forces between the block and the surface are considered to be negligible. Furthermore, the students pull the block-spring system 0.8 m from the systemβs equilibrium before they release the system so that it oscillates.

(i) Will this change in the experiment affect the value of the period of oscillation T for the block-spring system compared to the situation from part (a)? Briefly **state** your reasoning. (4pts)

- 1pt: No
- 1pt: T = 2Ο * sqrt(m/K)
- 1pt: The block is now horizontal, but the mass and spring constant are still the same.
- 1pt: From the equation, since gravity and amplitude don't matter, and since the mass and spring constant are the same, the period will not change.

**Part C**

(i) **Describe** an experimental procedure to determine whether or not the period of oscillation T for the block-spring system is different compared to the situation from part (a). **Include** any steps necessary to reduce experimental uncertainty. Give enough detail so that another student could replicate the experiment. As needed, include a diagram of the experimental setup. Assume equipment usually found in a school physics laboratory is available. (5pts)

- 1pt:
*Diagram above* - 1pt: Pull back the block so the stretch is 0.8m (measured by a meterstick).
- 1pt: Let go and time 10 oscillations (with a stopwatch).
- 1pt: Compare this period to the period found in (a)

- 1pt: Complete the results and average the resulting periods.

**Next Steps**

- π§ Want to continue reinforcing your knowledge of Unit 6? Check out Unit 6 Trivia, either
**as a document**or**as a game**. - π Want to review multiple units? Check out all of the
**AP Physics 1 FRQs**.

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