Best Examples of Physics Lab Report Examples: Simple Harmonic Motion

Most students don’t need another definition of SHM. They need examples of physics lab report examples: simple harmonic motion that show what a strong report actually looks like. So let’s start with concrete, lab‑bench reality.

Below are several realistic lab setups that instructors use in 2024–2025, and how a well‑written report might handle each one. You can lift the structure, style, and level of detail and adapt it to your own lab.

Example of a Classic Mass–Spring SHM Lab Report

In many first‑year physics courses, the example of an SHM lab you’ll see first is the vertical mass–spring system.

Typical Aim

To determine the spring constant \(k\) using static measurements and verify the SHM model by comparing the theoretical period \(T = 2\pi \sqrt{m/k}\) with measured oscillation periods.

Core Experimental Steps (described in prose)

In a strong report, the procedure section doesn’t read like a recipe. Instead of bullet points, you explain what you did and why. For example:

A helical steel spring was suspended from a rigid support. Small masses from 50 g to 250 g were attached in 50 g increments. For each mass, the equilibrium extension relative to the unloaded spring was measured with a meter stick. After determining the spring constant from the force–extension data, the 150 g mass was displaced about 3 cm from equilibrium and released. Ten consecutive oscillations were timed using a digital stopwatch to reduce reaction‑time error, and the average period was calculated.

Sample Data and Analysis Narrative

A good example of analysis for this SHM report might say:

The force–extension graph was approximately linear over the tested range (50–250 g), with a best‑fit slope of \(k = (9.8 \pm 0.2)\,\text{N/m}\). Using this value, the theoretical period for \(m = 0.150\,\text{kg}\) is

\[ T_\text{theory} = 2\pi \sqrt{\frac{0.150}{9.8}} = 0.78\,\text{s}. \]

Experimentally, timing 10 oscillations gave \(T_\text{exp} = (0.81 \pm 0.02)\,\text{s}\). The percent difference between theory and experiment is about 3.8%, which is comparable to the estimated timing uncertainty and the uncertainty in the mass.

This kind of paragraph shows your instructor you can connect equations to real measurements rather than just quoting formulas.

Example of a Simple Pendulum SHM Lab Report

Another of the best examples of physics lab report examples: simple harmonic motion is the simple pendulum. Even though the motion is only approximately SHM for small angles, it’s perfect for learning how to discuss assumptions.

Aim and Model

To measure the period of a simple pendulum as a function of length and compare the results with the theoretical relation \(T = 2\pi \sqrt{L/g}\) under the small‑angle approximation.

How a Strong Methods Section Sounds

A small brass bob (50 g) was attached to a light, inextensible string and suspended from a rigid support. The length \(L\) was measured from the suspension point to the center of the bob. Lengths from 0.20 m to 1.00 m were tested in 0.20 m increments. For each length, the bob was displaced by approximately 5° from the vertical and released without push. The time for 20 oscillations was recorded using a digital stopwatch, and the period was obtained by dividing by 20.

Data Discussion

Instead of dumping a table and calling it a day, a good report interprets the data:

A plot of \(T^2\) versus \(L\) produced a straight line, supporting the SHM prediction. Linear regression gave a slope of \((4.02 \pm 0.10)\,\text{s}^2/\text{m}\), corresponding to an effective gravitational acceleration \(g = (9.81 \pm 0.24)\,\text{m/s}^2\), consistent with the accepted value near the Earth’s surface reported by NIST (nist.gov). Deviations at the shortest length (0.20 m) were larger, likely due to timing uncertainty and the finite size of the bob.

This example shows how to compare with an accepted constant using an external reference.

Lab Report Examples Include Damped SHM and Energy Analysis

Modern courses are increasingly asking for examples of physics lab report examples: simple harmonic motion that go beyond ideal, undamped motion. In 2024–2025, many lab manuals now include:

Example: Damped Mass–Spring Oscillator

Here’s how a clear report might frame a damping experiment:

The motion of a 200 g mass attached to a vertical spring was recorded using a motion sensor connected to a computer‑based data acquisition system. A small cardboard disk was attached to the mass to increase air resistance. Position–time data were collected for about 20 oscillations. The amplitude was extracted from the peaks of the displacement graph and plotted versus time. The envelope was fit to an exponential decay \(A(t) = A_0 e^{-bt/2m}\) to obtain the damping coefficient \(b\).

Then, in the discussion:

The amplitude decreased approximately exponentially with time, with a best‑fit damping coefficient \(b = (0.15 \pm 0.02)\,\text{kg/s}\). The damped angular frequency \(\omega_d\) was only slightly lower than the undamped \(\omega_0\), consistent with the underdamped regime described in standard mechanics texts, such as those used in introductory physics courses at MIT (ocw.mit.edu).

Example: Energy in Simple Harmonic Motion

Another of the best examples you might be assigned is an energy‑focused SHM lab:

Using a motion sensor, the position and velocity of a glider attached to a spring on an air track were recorded. From these, the kinetic energy \(K = \tfrac{1}{2} m v^2\) and spring potential energy \(U = \tfrac{1}{2} k x^2\) were computed at each time step. A graph of \(K\), \(U\), and total mechanical energy \(E = K + U\) versus time was produced.

A strong conclusion paragraph might say:

The total mechanical energy remained approximately constant over several periods, varying by less than 5%, while kinetic and potential energies exchanged smoothly with a phase difference of about \(\pi/2\). The gradual decrease in total energy over longer times is consistent with non‑conservative forces such as air resistance and friction in the air‑track supports.

This is exactly the kind of example of interpretation that separates an A‑level report from a B‑level one.

Real Examples: Modern SHM Labs Using Sensors and Apps

If your course uses modern equipment, your instructor may expect real examples of physics lab report writing that mention digital tools, not just stopwatches.

Example: Smartphone Accelerometer SHM Lab

Many universities now let students attach a smartphone to a mass–spring system or a swinging platform and use an accelerometer app:

A smartphone was securely attached to a cart connected to a horizontal spring. Using a free accelerometer app, acceleration data along the direction of motion were recorded at 100 Hz while the cart oscillated. The acceleration signal was exported and analyzed in a spreadsheet. A sinusoidal fit yielded the angular frequency, which was compared to \(\omega = \sqrt{k/m}\) obtained from static spring measurements.

Here’s how you might describe the results:

The accelerometer data showed a nearly sinusoidal pattern with an angular frequency \(\omega_\text{fit} = (6.25 \pm 0.05)\,\text{rad/s}\), in good agreement with \(\omega_\text{theory} = (6.30 \pm 0.10)\,\text{rad/s}\). The phase and amplitude were sensitive to the initial displacement, but the frequency remained essentially constant, illustrating a defining property of simple harmonic motion.

Example: Video Tracking of a Pendulum

Another modern example of SHM reporting uses video analysis software like Tracker:

A pendulum was recorded using a smartphone at 60 frames per second. The video was imported into Tracker, and the bob position was marked frame by frame. The horizontal displacement versus time was extracted and fit to a sinusoidal function. The period obtained from the fit was compared with the period measured by timing 20 oscillations with a stopwatch.

In your discussion, you might compare methods:

The period from video analysis, \(T_\text{video} = (1.98 \pm 0.01)\,\text{s}\), agreed within 1% with the stopwatch measurement, \(T_\text{manual} = (2.00 \pm 0.03)\,\text{s}\). The smaller uncertainty in \(T_\text{video}\) reflects the higher time resolution of the camera and the absence of human reaction‑time error.

These real examples show your instructor that you understand how technology affects your uncertainty and data quality.

How to Structure Your Own SHM Report Using These Examples

When you look at all these examples of physics lab report examples: simple harmonic motion, some patterns jump out. Strong reports:

• State a clear, measurable aim (find \(k\), verify \(T \propto \sqrt{m}\) or \(T \propto \sqrt{L}\), estimate \(g\), determine damping).
• Link every equation to actual measurements.
• Talk explicitly about sources of error and how they affect the results.

Introduction Section

A solid introduction for any SHM lab typically:

• Briefly explains the physical system (mass–spring, pendulum, air‑track glider).
• States the SHM model: restoring force proportional to displacement, \(F = -kx\) or \(\tau = -mgL\theta\) for small angles.
• Mentions the key equation you’re testing, such as \(T = 2\pi \sqrt{m/k}\) or \(T = 2\pi \sqrt{L/g}\).
• Explains why the experiment matters: for example, measuring \(g\), checking Hooke’s law, or exploring energy conservation.

You can literally borrow the structure from any example of SHM report above and rewrite it in your own voice.

Methods and Data

Instead of step‑by‑step bullets, describe what you did as a short story of the experiment:

The spring constant was first determined by hanging known masses and recording the resulting extension. After confirming that the force–extension graph was linear, a 200 g mass was chosen for the oscillation study. The mass was displaced approximately 4 cm from equilibrium and released. Ten oscillations were timed for three separate trials.

For data, your instructor wants to see:

• Raw measurements (mass, length, period, amplitude) organized clearly.
• Any calculations (such as \(k\), \(T\), \(g\), \(\omega\)) explained in words and equations.
• Graphs described in text: “The plot of \(T^2\) vs \(L\) was linear, indicating…” rather than just pasted.

Discussion and Conclusion

This is where many students lose points. Use the examples of physics lab report examples: simple harmonic motion above as a checklist:

• Compare measured values to theoretical predictions or accepted constants.
• Quote uncertainties and percent differences.
• Explain why differences exist: timing error, angle too large, friction, non‑linear springs, sensor calibration.
• State whether the data support the SHM model within experimental uncertainty.

A strong closing sentence might be:

Overall, the measured periods agreed with the SHM prediction within 4–5%, supporting the validity of the simple harmonic model for small displacements in the tested range.

Current Trends (2024–2025) in SHM Lab Assignments

Physics education research over the last few years has pushed labs toward more real‑world context and more analysis of uncertainty rather than cookbook verification. That means the best examples of physics lab report examples: simple harmonic motion now often:

• Use sensors (motion detectors, smartphones, photogates) instead of only stopwatches.
• Ask students to fit data using software (Excel, Python, Logger Pro, Tracker) and interpret fit parameters.
• Emphasize error analysis and model limitations, not just “we got the right number.”

If you want to see how universities frame SHM experiments, open‑access course materials from places like MIT and other institutions on ocw.mit.edu or physics.nist.gov give a sense of modern expectations.

When you write, let these real examples guide your structure, but make sure your numbers, uncertainties, and wording come from your own lab work.

FAQ: Simple Harmonic Motion Lab Report Examples

Q1: Where can I see more examples of physics lab report examples: simple harmonic motion?
Many university physics departments post sample lab manuals or student reports online. Look for open‑course materials from major schools like MIT or state universities. You can also search for “introductory mechanics lab manual PDF” from .edu sites and focus on the oscillations or SHM sections.

Q2: What is a good example of an SHM research question for a lab report?
A strong example of a research question is: “How well does the measured period of a mass–spring system follow \(T = 2\pi \sqrt{m/k}\) over the mass range 50–300 g?” or “Does the period of a pendulum depend on amplitude for angles between 5° and 25°?” These questions are specific and test a clear prediction.

Q3: Do I always need to include damping in my SHM lab report?
Not necessarily. Many introductory labs focus on undamped SHM first. However, even if your procedure doesn’t explicitly study damping, you should acknowledge that real systems lose energy and that small deviations from theory may come from friction and air resistance.

Q4: How detailed should the error analysis be in a simple harmonic motion report?
At minimum, estimate uncertainties in your key measurements (mass, length, time) and show how they affect quantities like \(T\), \(k\), or \(g\). Comment on which source dominates. For example, in a pendulum lab, timing error usually matters more than length measurement error.

Q5: Can I reuse structure from online SHM lab report examples?
Yes, you can model your structure—introduction, methods, results, discussion—on examples of good reports, but your data, calculations, and wording must reflect your own experiment. Instructors are very familiar with common templates and will notice copy‑paste text.