Simple Pendulum Lesson Plan with a Virtual Lab
Updated 2026-10-02
This simple pendulum lesson plan uses a free virtual lab so students can find out, in one class period, what really sets the period of a pendulum. They test mass, length, amplitude and gravity one at a time, plot T² against length and calculate g from the slope. Everything is ready to use: learning goals, setup, predictions, a step-by-step activity with the values students should get, a five-question set you can attach to the class link, an extension on a mystery planet, and ideas for differentiation. Every number comes from the simulation's own model.
Lesson at a glance
- Level: grades 9–12 (ages 14–18), physics or physical science.
- Time: one 50–60 minute period, plus an optional 20-minute extension.
- Prior knowledge: period and frequency, square roots, plotting a straight-line graph.
- Format: pairs on laptops, tablets or phones, or the whole class with one projector.
- Simulation: Simple pendulum – period, energy and measuring g.
Learning goals
By the end of the lesson, students can:
- Show that the period of a pendulum does not depend on the mass of the bob.
- Show that the period is proportional to √L: four times the length gives twice the period.
- Plot T² against L and find g from the slope, using T = 2π√(L/g).
- Explain why a large swing makes the period slightly longer than the formula predicts.
- Predict how the period changes on the Moon or Jupiter.
What the simulation does
The simulation has three screens:
- Intro: one pendulum, or two side by side with Two pendulums. Each has a length slider (0.1–2.0 m) and a mass slider (0.1–2.0 kg), both in steps of 0.1. Gravity offers Earth (9.8 m/s²), Moon (1.62), Jupiter (24.79) or Planet X (1–30 m/s²). Friction is None, Low or High. Tick boxes add a Ruler, a Stopwatch, a Period timer and v/a vectors.
- Energy: bars for KE, PE and thermal energy in joules, released from 30°.
- Lab: a mystery planet with a hidden g. Students measure the period, type their value of g and press Check. It counts as correct within 5%.
Three details matter before you teach with it:
- It is not the small-angle model. The simulation solves the full equation with sin θ. On the Intro screen the pendulum starts at 20°, so every period is about 0.8% longer than 2π√(L/g). That is a feature: it gives you a real systematic error to discuss.
- Press Reset after changing the length. The slider changes the length mid-swing and keeps the current angle and speed, so the amplitude changes. Reset releases both pendulums from 20° again.
- The period timer reads to 0.01 s. It times each full swing on screen frames, so a reading can flicker by 0.01 s, occasionally 0.02 s, from one swing to the next. Tell students to record the value that appears most often.
Materials and setup before class
Materials: one device per pair (or a projector), the data table on paper or in a spreadsheet, graph paper and a calculator.
Setup (10 minutes, once):
- Open the simulation on the Intro screen: Earth, friction None, pendulum 1 at 1.0 m and 1.0 kg. These are the defaults.
- Click Share and create a link for each class, for example "Physics · Period 3". The link pins these starting values.
- Optional: on the Questions tab, enter the question set below and attach it to the link.
- Post the link, or open it in present mode and show the QR code.
On an ordinary link, students can see and change every starting value in the panel under the simulation, including the mystery planet and Show the answer for g (Lab). That doesn't matter for the Intro lesson. For the Lab extension, hide them with locked parameters, a Pro link option, or trust students not to peek.
Lesson sequence
1. Hook and predictions (7 minutes)
Project the pendulum swinging and ask what controls how fast it swings. Collect ideas on the board. Then have them commit to two predictions, on paper or on the link:
- P1. "Two pendulums are both 1.0 m long. One bob is 0.5 kg, the other 2.0 kg. Which one swings back and forth faster?"
- P2. "You make a pendulum four times longer, from 0.4 m to 1.6 m. The period… stays the same / doubles / quadruples / halves."
Most students expect the heavy bob to swing faster, and many pick "quadruples" for P2. Don't correct anyone yet.
2. Does mass matter? (6 minutes)
Pairs tick Two pendulums, set both lengths to 1.0 m, set the masses to 0.5 kg and 2.0 kg, and press Reset. The two bobs swing in step, swing after swing. Turn on the Period timer for each one in turn: both read 2.02 s (sometimes 2.03 s).
Ask: "Why doesn't the heavier bob win?" A heavier bob needs more force to speed it up, and gravity pulls on it with exactly that much more force. The mass cancels.
3. Length and period: collect data (15 minutes)
Untick Two pendulums. Pairs keep 1.0 kg, Earth and no friction. For each length they move the slider, press Reset, tick Period timer and wait for two readings. The last column is for you; leave it blank on the student copy.
| L (m) | T (s) | T² (s²) | Expected T (s) | Expected T² (s²) |
|---|---|---|---|---|
| 0.2 | 0.90–0.92 | 0.82 | ||
| 0.4 | 1.28 | 1.64 | ||
| 0.8 | 1.81 | 3.27 | ||
| 1.0 | 2.02 | 4.09 | ||
| 1.6 | 2.56 | 6.55 | ||
| 2.0 | 2.86 | 8.18 |
Readings within ± 0.02 s of the expected period are fine. Then ask pairs for two patterns. Good answers: "From 0.4 m to 1.6 m the period goes from 1.28 s to 2.56 s, exactly double" and "T² divided by L is about 4.1 every time."
Check P2 now. Four times the length gives twice the period because T depends on √L.
4. Graph T² against L and find g (10 minutes)
Students plot T² (vertical) against L (horizontal). The points form a straight line through the origin with a slope of about 4.09 s²/m.
Since T = 2π√(L/g), squaring gives T² = (4π²/g)·L. So:
- slope = 4π²/g, which means g = 4π² ÷ slope = 39.48 ÷ 4.09 ≈ 9.65 m/s².
That is about 1.5% below the 9.8 m/s² the simulation uses. Ask students where the error comes from. It isn't random: every period is slightly long because the pendulum swings to 20°, so every T² is too big and g comes out too small. Repeating the measurement won't fix it.
To test the idea, set L = 1.0 m and drag the bob out to about 5° (the angle readout shows θ₁ while you drag). The period drops to about 2.01 s, close to the small-angle value of 2.007 s.
5. Amplitude and gravity (7 minutes)
Keep L = 1.0 m. Drag the bob to different angles and read the period:
| Release angle | about 10° | 20° | about 40° | about 60° | about 80° |
|---|---|---|---|---|---|
| Period (s) | 2.01 | 2.02 | 2.07 | 2.15 | 2.28 |
Dragging is never exact, so treat these as "about". The point is clear anyway: small swings barely change the period, while big swings make it noticeably longer. That is why clock pendulums swing through small angles.
Then press Reset and change Gravity. A 1.0 m pendulum has a period of about 4.97 s on the Moon and about 1.27 s on Jupiter. Ask: "How much weaker is the Moon's gravity, and how much longer is the period?" 9.8 ÷ 1.62 = 6.05, and √6.05 = 2.46, so the period is 2.46 times longer: 2.02 × 2.46 ≈ 4.97 s.
6. Exit check (5 minutes)
Use questions 3–5 of the set below, or ask on paper: "A pendulum has a period of 2.86 s on Earth. How long is it?" (2.0 m). Then open View answers and show the Prediction and After columns for P1 and P2 side by side.
Question set for this lesson
Enter these on the simulation's Questions tab. Suggested Instructions for students: "Use the Intro screen. Change one thing at a time. After changing the length, press Reset. Use the Period timer for every reading."
1. Multiple choice · Before, as a prediction · Ask again after the simulation
- Question: "Two pendulums are both 1.0 m long. One bob is 0.5 kg, the other 2.0 kg. Which one swings back and forth faster?"
- Options: The 0.5 kg bob / The 2.0 kg bob / Both take the same time (correct) / It depends on the angle
- Explanation: "Without friction, mass cancels out. A heavier bob needs a bigger force to speed up, and gravity pulls on it with exactly that bigger force. The period depends only on the length and on g, so both pendulums stay in step."
2. Multiple choice · Before, as a prediction · Ask again after the simulation
- Question: "You make a pendulum four times longer, from 0.4 m to 1.6 m. The period…"
- Options: stays the same / doubles (correct) / quadruples / halves
- Explanation: "The period depends on the square root of the length: T = 2π√(L/g). Four times the length gives √4 = 2 times the period. In the simulation, 1.28 s becomes 2.56 s."
3. Number · After the simulation
- Question: "Set L = 1.0 m on Earth with no friction. Press Reset and turn on the Period timer. What is the period?"
- Answer: 2.02, tolerance ± 0.03, unit s
- Explanation: "The formula 2π√(1.0/9.8) gives 2.01 s. The simulation starts the swing at 20° and uses the full model, so the period is about 0.8% longer: 2.02 s. The timer can flicker by 0.01 s between swings."
4. Number · After the simulation
- Question: "Plot T² against L from your table. Use T² = (4π²/g)·L to calculate g."
- Answer: 9.7, tolerance ± 0.2, unit m/s²
- Explanation: "The slope of the T²–L graph is about 4.09 s²/m, so g = 4π² ÷ 4.09 ≈ 9.65 m/s². It is a little below 9.8 because the 20° swing makes every period slightly too long. That is a systematic error: repeating the measurement does not remove it."
5. Short answer · After the simulation
- Question: "On the Moon, the same 1.0 m pendulum has a period of about 4.97 s. Explain why it is longer than on Earth."
- Accepted answers (optional): *gravity*
- Model answer: "The Moon's gravity is weaker (1.62 m/s² instead of 9.8 m/s²), so the force pulling the bob back is smaller and it speeds up more slowly. The period is proportional to 1/√g: √(9.8/1.62) ≈ 2.46, and 2.02 s × 2.46 ≈ 4.97 s."
Questions 1 and 2 are the predictions, asked again after the simulation so students can compare. The formative assessment guide explains how to read the results across classes.
Extension: the mystery planet and energy
Lab screen (20 minutes). The pendulum swings from 8° on a planet with a hidden g. Students measure the period at two or three lengths, calculate g = 4π²L/T² and press Check. Give each class a different planet by pinning it on the link:
| Planet | Period at 1.0 m (s) | Period at 2.0 m (s) | g (m/s²) |
|---|---|---|---|
| A | 3.03 | 4.29 | 4.3 |
| B | 1.77 | 2.51 | 12.6 |
| C | 1.40 | 1.98 | 20.1 |
| D | 2.31 | 3.27 | 7.4 |
The Lab readout flickers by up to 0.02 s on the faster planets, which is still well inside the 5% the Check button accepts. For a full lab write-up with uncertainties, see the measuring g lab in how to create a virtual lab activity.
Energy screen (10 minutes). At 1.0 m, 1.0 kg and 30°, the PE bar starts at 1.31 J. At the bottom it has all turned into KE. Double the mass or the length and the energy doubles to 2.63 J. Switch Friction to Low and watch the thermal bar grow while the total stays the same.
Friction and mass. Here is a twist for strong students. On the Intro screen, tick Two pendulums, set both to 1.0 m, the masses to 0.5 kg and 2.0 kg, Friction Low, and press Reset. After about ten seconds the heavy bob still swings to about 18°, the light one only to about 13°. Mass doesn't change the period, but with friction it changes how long the swinging lasts.
Differentiation
Support:
- Give the table with the lengths filled in and use only 0.4, 1.0 and 1.6 m.
- Skip T² and have students compare periods directly: "0.4 m to 1.6 m: how many times longer is the period?"
- Give sentence starters: "When the length is four times bigger, the period…"
- Pair students so one sets the length and presses Reset while the other reads the timer.
Stretch:
- Derive g = 4π²L/T² before measuring, then explain why the 20° swing makes it too small.
- Calculate the length that gives a period of exactly 1.00 s on Earth (0.25 m from the formula). The slider moves in 0.1 m steps, so check that 0.2 m (about 0.91 s) and 0.3 m (about 1.11 s) land on either side.
- Use Planet X to find which g makes a 1.0 m pendulum take 2.86 s, the same as 2.0 m on Earth (4.9 m/s², half of Earth's).
English learners: the simulation is available in six languages. Create a second link in the student's language so the labels are familiar while the discussion stays in English.
Standards alignment
This lesson fits the oscillations or simple harmonic motion unit of a high school physics course, such as AP Physics 1 or the oscillations topic of A-level Physics. NGSS has no performance expectation dedicated to pendulums, so we don't claim one. The lesson does exercise three NGSS practices: Planning and Carrying Out Investigations, Analyzing and Interpreting Data, and Using Mathematics and Computational Thinking.
For more ideas in this unit, see interactive physics lesson ideas. For general classroom routines, see how to use interactive simulations in the classroom.
FAQ
Why is the period 2.02 s and not 2.01 s for a 1 m pendulum?
The formula T = 2π√(L/g) is only exact for very small swings. The simulation starts at 20° and solves the full equation, so the period is about 0.8% longer. Drag the bob to about 5° and you get close to 2.01 s.
Why does the period timer change by 0.01 s between swings?
It times each swing on screen frames, so the last digit can flicker. Record the value that appears most often, or time ten swings with the stopwatch and divide by ten.
Does the mass ever matter?
Not for the period without friction. With friction on, a heavier bob loses its swing more slowly, because the same friction force slows a larger mass less.
Can students do this lesson on phones?
Yes. Students open the link without an account, and the sliders and dragging work on touch screens. A tablet or laptop makes it easier to read the timer and fill in the table.