Eight experiments with the FizziQ Web Simulation module

Galileo's pendulum, astronaut centrifuge, Boyle's law, waves on a lake: these are classic physics experiments that would be interesting to perform with real equipment such as a smartphone, but that sometimes cannot be carried out physically. That is why we created a simulation tool within FizziQ Web — not to replace experimentation in the physical world, which remains the only truly relevant approach for analysing the world around us, but to make experimentation easier when it cannot be done for real. In this article, we present eight ready-to-use activities covering mechanics, thermodynamics and waves, from the simple pendulum to the optimal launch angle of a projectile.

Table of contents: The Simulation module: a virtual laboratory with real tools · The simple pendulum: from Galileo to Huygens' clocks · The spring oscillator: discovering T = 2π√(m/k) · The centrifuge: centripetal acceleration and g-force · The optimal launch angle: ballistics at your fingertips · Boyle's law: when PV stays constant · Gay-Lussac's law: towards absolute zero · Waves and frequency: verifying v = λ × f · Wave attenuation: why ripples fade · Conclusion

The Simulation module: a virtual laboratory with real tools

The principle behind the FizziQ Web Simulation module is simple, but we hope it will prove useful to teachers and consistent with the founding principles of inquiry-based learning: the simulations reproduce the real world, and students have the same tools as an experimenter facing a real physical phenomenon. They can place virtual sensors, start a recording, watch data appear in real time, then analyse their measurements in the FizziQ experiment notebook. The key difference is that the experiment takes place in a virtual, controlled and reproducible environment, accessible from any computer, tablet or smartphone with a web browser.

What sets this approach apart from many other simulation tools is that the data acquisition and analysis workflow is identical to the one students would use with the built-in sensors of their smartphone, with a microcontroller, or with FizziQ Connect external sensors. Students record measurements, add them to their experiment notebook, plot graphs, perform curve fitting, and export their results — just as they would with real sensors. The experimental process stays the same: only the data source changes. This pedagogical continuity matters. A student who has learned to analyse the oscillations of a virtual pendulum will be able to transfer those skills directly when using a real pendulum with a smartphone accelerometer. Conversely, a student already familiar with smartphone sensors will find their way easily in the simulation environment.

Simulations also offer practical pedagogical advantages that the real world does not always allow. You can vary a single parameter at a time with good precision — adjust the length of a pendulum to the nearest centimetre, change the stiffness of a spring without changing the mass, set the temperature of a gas to a specific value. You can repeat an experiment as many times as needed, without losing time or consuming materials. You can explore situations that would be difficult or unsafe in a laboratory — a ten-metre pendulum, a centrifuge at 60 revolutions per minute, compressing a gas to a third of its initial volume. And above all, students can focus on the physics rather than on the setup: there is no need to attach a spring to the ceiling or calibrate a pressure gauge, so all attention can go to understanding the phenomenon.

The FizziQ Web Simulation module currently offers six simulation environments: Pendulum, Spring Oscillator, Centrifuge, Ballistics, Ideal Gas, and Waves on a Lake. Each environment comes with guided activities and detailed experiment sheets that teachers can distribute directly to their students. Let us now look at these eight activities in detail.

1. The simple pendulum: from Galileo to Huygens' clocks

Experiment sheet: Simple pendulum

Duration: 35 minutes

Level: High school

Simulation: Pendulum

According to legend, Galileo discovered the isochronism of the pendulum by watching a chandelier swing in the cathedral of Pisa. He noticed that, regardless of the amplitude of the oscillations, the period remained the same. This property — that the period does not depend on the amplitude for small oscillations — is the basis of pendulum clocks, invented by Christiaan Huygens in 1656. But what does the period depend on?

In 1659, Huygens determined the exact expression: T = 2π√(L/g), where L is the length of the string and g the acceleration due to gravity. This formula shows two things: the period depends neither on the mass of the pendulum nor on the amplitude of its oscillations (as long as it remains small), but only on the length of the string and on gravity. The pendulum then became the first precise instrument for measuring the constant g. In 1690, Huygens reported that the length of a pendulum beating the second in Paris was 0.9941 m, corresponding to a gravitational acceleration of 9.812 m/s².

In this activity, students use the FizziQ Web Pendulum simulation to measure the period of oscillations while systematically varying the string length, then the initial angle. By plotting T² against L, they obtain a straight line with a slope of 4π²/g, which allows them to determine the acceleration due to gravity. They also check that the period is nearly constant from 5° to 20°, but increases noticeably beyond that: at 45°, the deviation is already 3.5%, and at 90° it reaches 17%. Isochronism is therefore only valid for small oscillations — a subtlety that the simulation makes easy to explore quantitatively, something that is hard to do with a real pendulum where the initial angle is difficult to control precisely.

Why this activity is useful in the classroom: it allows students to work simultaneously on the concept of period, the linearisation of a physical law (going from T(L) to T²(L)), the experimental determination of a physical constant, and the limits of validity of a model — all in 35 minutes.

2. The spring oscillator: discovering T = 2π√(m/k)

Experiment sheet: Oscillator period

Duration: 35 minutes

Level: High school

Simulation: Spring oscillator

Attach a mass to a spring, pull it down and release: the mass oscillates. But what determines the speed of these oscillations? If you use a stiffer spring, do the oscillations get faster or slower? And if you attach a heavier mass? These straightforward questions lead to one of the most widely used formulas in physics: T = 2π√(m/k), the period of the harmonic oscillator.

The harmonic oscillator is a model that extends well beyond the simple spring. It describes the oscillations of a quartz crystal in a watch, the vibrations of a diatomic molecule, the oscillations of an LC circuit in electronics, and — in a quantum context — the energy levels of photons. Understanding the behaviour of a mass-spring oscillator provides intuition that is useful across many areas of physics.

The activity is structured in three parts. First, students vary the mass at constant stiffness (k = 20 N/m) and measure the period for masses ranging from 0.5 kg to 4.0 kg. The graph of T against m is a curve, but T² against m is a straight line with a slope of 4π²/k ≈ 1.97 s²/kg — confirming the quadratic relationship. Next, they vary the stiffness at constant mass and observe that T decreases as k increases: a stiffer spring oscillates faster. Finally, they verify a notable result of the harmonic oscillator: the period is independent of the amplitude. Whether the spring is pulled by 5 cm or 20 cm, the period remains the same.

Why this activity is useful in the classroom: in a real laboratory, it is difficult to have a range of springs with precisely known stiffness values. The simulation makes it possible to adjust k with precision and test many configurations in a few minutes, making accessible a parametric study that would otherwise require considerable equipment.

3. The centrifuge: centripetal acceleration and g-force

Experiment sheet: Centrifuge

Duration: 30 minutes

Level: High school

Simulation: Centrifuge

Astronauts train in large centrifuges that subject them to accelerations of 6 to 9 g, reproducing the forces felt during a rocket launch. Fighter pilots routinely experience 5 to 7 g in tight turns. Even on a fairground ride, accelerations of 3 to 4 g can be reached. But how is this acceleration calculated, and what parameters does it depend on?

The answer lies in the formula a = ω²r, where ω is the angular velocity in radians per second and r is the radius of the circular motion. This relationship shows that centripetal acceleration depends on the square of the angular velocity — doubling the rotation speed does not double the acceleration, it quadruples it. This quadratic dependence is what makes centrifuges so effective.

The activity asks students to verify this relationship in two steps. First, at a fixed radius (r = 5 m), they vary the rotation speed from 10 to 60 revolutions per minute and record the centripetal acceleration measured by the virtual sensor. The graph of a against ω² is a straight line with a slope equal to the radius — a direct demonstration of the formula. At 10 rpm, the acceleration is 5.5 m/s² (0.56 g), but at 60 rpm it reaches 197 m/s², or more than 20 g. Then, at a fixed speed (30 rpm), they vary the radius and verify the proportionality a = ω²r. They can then calculate the conditions needed to reach 3 g for a given radius, or determine the minimum radius of a ride to keep the acceleration below a comfort threshold.

Why this activity is useful in the classroom: it makes centripetal acceleration more concrete by connecting it to situations students are familiar with — fairground rides, spin dryers, astronaut training. Converting to g-forces creates a direct link to everyday experience.

4. The optimal launch angle: ballistics at your fingertips

Experiment sheet: Optimal launch angle

Duration: 30 minutes

Level: High school

Simulation: Ballistics

If you had to throw a ball as far as possible, at what angle would you throw it? Straight ahead? Up at 60°? At 45°? Artillery officers sought the answer to this question for centuries. Niccolò Tartaglia, a sixteenth-century Italian mathematician, was the first to show that a 45° angle maximises the range of a projectile. The rigorous proof came later with Galileo, who showed that the trajectory of a projectile is a parabola resulting from the combination of two independent motions: uniform horizontal motion and vertical free fall.

The range formula, R = v₀² × sin(2α) / g, yields a neat result. Since sin(2α) is at its maximum when 2α = 90°, that is α = 45°, this is indeed the angle that maximises range. But the formula also reveals a symmetry property: two complementary angles give exactly the same range. A shot at 30° reaches the same distance as a shot at 60°, a shot at 20° the same as a shot at 70°. This is because sin(2 × 30°) = sin(60°) = sin(120°) = sin(2 × 60°).

The activity has students launch projectiles at different angles (from 10° to 80° in steps of 10°) while keeping the same initial speed, then plot range against angle. The resulting curve is a bell shape, symmetric about 45°. For v₀ = 20 m/s, the maximum range at 45° is about 40.8 m. Students can also observe the visual difference between trajectories: low-angle shots are flat and fast, high-angle shots are tall and slow, yet certain pairs land at exactly the same point.

Why this activity is useful in the classroom: it connects an intuitive question (how do I throw the farthest?), an experimental observation (the bell curve), and a mathematical explanation (the sin(2α) function). Students see that mathematics accounts for a result they can observe directly.

5. Boyle's law: when PV stays constant

Experiment sheet: Boyle's law

Duration: 25 minutes

Level: High school

Simulation: Ideal gas

In 1662, Robert Boyle discovered that when a gas is compressed at constant temperature, the pressure increases in inverse proportion to the volume. In other words, the product PV stays constant. Twenty years later, the French physicist Edme Mariotte independently arrived at the same law, which is why in France the law bears both their names.

This law follows directly from the ideal gas model, PV = nRT. At constant temperature T and constant amount of substance n, the product PV is indeed a constant. At the molecular level, the explanation is straightforward: when the volume is reduced, gas molecules have less space, they hit the walls more frequently, and the pressure increases. If the volume is halved, each molecule strikes the walls twice as often, and the pressure doubles.

In the FizziQ Web Ideal Gas simulation, students keep the temperature constant and slowly move the piston to vary the volume while recording both pressure and volume simultaneously. The resulting P(V) graph is a hyperbola, characteristic of inverse proportionality. To linearise the relationship, students then plot P against 1/V and obtain a straight line through the origin with a slope of nRT. They can verify that the product PV is constant for each pair of measurements: if the volume goes from 0.06 m³ to 0.02 m³, the pressure triples.

Why this activity is useful in the classroom: carrying out an isothermal transformation with a real gas is a significant technical challenge (sealing, thermalisation, accurate pressure readings). The simulation removes these difficulties and lets students focus on the physical relationship. It is also a good opportunity to practise linearising a hyperbola, a useful cross-disciplinary mathematical skill.

6. Gay-Lussac's law: towards absolute zero

Experiment sheet: Gay-Lussac (simulated)

Duration: 25 minutes

Level: High school

Simulation: Ideal gas

What happens when you heat a gas enclosed in a rigid container? The pressure rises. But how exactly? In 1802, Joseph Louis Gay-Lussac found that the pressure of a gas at constant volume is proportional to its absolute temperature. This law has a far-reaching consequence: it predicts the existence of a lowest possible temperature, a temperature at which the pressure would reach zero. This is absolute zero, −273.15 °C or 0 K.

The idea is worth pausing on. By extrapolating the P(T) line towards low temperatures, one reaches a point where the pressure would become zero — meaning the gas molecules would stop moving entirely. No real gas remains gaseous down to this temperature (it liquefies well before), but the extrapolation gives a good estimate of absolute zero. It is a clear example of a theoretical prediction derived from a simple experimental measurement.

Students use the simulation with the piston locked (constant volume) and slowly vary the temperature. By plotting P against T (in kelvins), they obtain a straight line through the origin, confirming the proportionality P = (nR/V) × T. If they plot the graph in degrees Celsius, the line crosses the temperature axis at −273 °C when P = 0: they have just estimated absolute zero from a graph alone. The pressure increases by about 0.37% per degree Celsius, or roughly 22% between 0 °C and 60 °C.

Why this activity is useful in the classroom: estimating absolute zero by graphical extrapolation is a memorable moment for students. They realise that a simple measurement (pressure and temperature) can predict a fundamental constant of nature. It illustrates well what the scientific method can achieve.

7. Waves and frequency: verifying v = λ × f

Experiment sheet: Waves and frequency

Duration: 25 minutes

Level: High school

Simulation: Waves on a lake

Throw a pebble into a lake and watch the circular waves spread across the surface. Does their propagation speed depend on the frequency? On the amplitude? Answering these questions leads to one of the most widely applicable relationships in wave physics: v = λ × f, where v is the wave speed, λ the wavelength and f the frequency. This relationship applies equally to sound waves, light waves, seismic waves and radio waves. It runs through the entire study of wave phenomena.

The FizziQ Web Waves on a Lake simulation lets students control three parameters precisely: frequency, amplitude and propagation speed. Buoys placed at different distances from the source measure the water height as the wave passes, making it possible to visualise the wave motion in real time.

Students fix the propagation speed (for example v = 2 m/s) and vary the frequency from 0.5 Hz to 3.0 Hz. For each frequency, they measure the distance between two successive crests, that is, the wavelength λ. The results are clear: λ = 4.0 m for f = 0.5 Hz, λ = 2.0 m for f = 1.0 Hz, λ = 1.0 m for f = 2.0 Hz… The product λ × f equals 2.0 m/s for every measurement, confirming that the speed is constant and independent of frequency. By plotting λ against 1/f, students obtain a straight line through the origin with a slope of v = 2.0 m/s.

Why this activity is useful in the classroom: the relationship v = λf is often taught in an abstract way. Here, students discover it through direct observation: they see the waves get closer together as the frequency increases, they measure this change, and they derive the law. This is what experimental inquiry is about.

8. Wave attenuation: why ripples fade

Experiment sheet: Wave attenuation

Duration: 25 minutes

Level: High school

Simulation: Waves on a lake

When you throw a stone into a lake, the waves are strong near the point of impact, then weaken as they move away. Why does the wave lose amplitude? Is it because it loses energy, or because that energy spreads over an increasingly wide wavefront? This question touches on a fundamental principle: the conservation of energy.

For a circular wave propagating in two dimensions (like a ripple on a lake surface), the energy emitted by the source spreads over a circle whose circumference grows proportionally with distance r. Since the energy of a wave is proportional to the square of its amplitude, it follows that the amplitude decreases as 1/√r. This is not a loss of energy — total energy is conserved — but a geometric spreading. By comparison, a spherical wave in three dimensions (like sound in air) decreases as 1/r, because the energy spreads over a sphere whose surface area grows as r².

Students place buoys at different distances from the source and record the vertical motion of each buoy. They measure the amplitude of the oscillations and plot A against r: the curve decreases, but not linearly. By plotting A against 1/√r, they obtain a straight line through the origin — confirming the geometric attenuation law. The activity also allows them to check a subtle point: the frequency of the oscillations is the same for all buoys, regardless of their distance from the source. Only the amplitude decreases, not the frequency. If the initial amplitude is doubled, the amplitudes at each distance are doubled as well, but the shape of the decrease remains the same.

Why this activity is useful in the classroom: it develops both a qualitative and quantitative understanding of attenuation, clearly distinguishing geometric attenuation (energy spreading) from absorption (energy dissipated as heat). Linearising with 1/√r is a good exercise in data processing.

Conclusion

The eight activities presented here are a sample of what the FizziQ Web Simulation module can offer. They cover a broad range of the high school physics curriculum — oscillations and mechanics with the pendulum, oscillator and centrifuge, kinematics with ballistics, thermodynamics with gas laws, and wave phenomena with lake waves — while each remaining accessible in 25 to 35 minutes.

The pedagogical value of these simulations goes beyond illustrating a lesson. By placing students in the role of the experimenter — choosing parameters, recording measurements, plotting graphs and checking a law — they build transferable skills: rigour in data collection, curve linearisation, the concept of a control variable, and critical analysis of results. And because the FizziQ experiment notebook works in the same way whether the data comes from a simulation, from a smartphone's sensors, or from external sensors, these skills transfer directly to the real laboratory.

We invite you to try these activities with your students. Each experiment sheet is ready to use and can be handed out as is. And if your students ask "is this real?", you can tell them that the physical laws they have verified are the same ones that govern the real world — and that this is precisely the point of a good simulation.

Resources:

• FizziQ Web

• All FizziQ activities