Oscillations & Waves
Oscillations & Waves is a free interactive simulation from StudyFi Lab. It runs right in your browser, with no sign-up and nothing to install.
Pendulums, springs, waves and interference
Experiments
Simple pendulum
A bob on a string of length L swings under gravity according to θ″ = −(g/L)·sin θ. For small angles T = 2π√(L/g), and the period does not depend on the amplitude. At large angles the actual period is longer. Energy flows between kinetic and potential, while the total stays the same.
Try this: Pull the bob to 10°, then to 80°, and compare the measured period with 2π√(L/g).
Mass on a spring
A spring of stiffness k pulls a mass m back to equilibrium, and the damping b slows it: x″ = −(k/m)·x − (b/m)·x′. Without damping it oscillates with T = 2π√(m/k). At b = 2√(km) (critical damping) it returns fastest without overshooting; with larger b it creeps back more slowly. Damping gradually removes energy.
Try this: Set the damping with the “Critical” button, then double b — which return to the centre is faster?
Travelling wave
The wave y = A·sin(kx − ωt + φ) moves to the right at v = λ·f, where λ is the wavelength (the distance between two neighbouring crests) and f is the frequency. The marked particle only moves up and down — the wave carries energy, not matter.
Try this: Double the frequency and watch how the speed v changes. Then double the wavelength.
Standing wave on a string
A string of length L fixed at both ends can only vibrate so that a whole number of half-wavelengths fits on it: λₙ = 2L/n. Hence fₙ = n·v/(2L), where v is the wave speed on the string. The nodes (points at rest) lie at x = kL/n, with the antinodes of largest amplitude between them.
Try this: Switch from the 1st to the 2nd and 3rd harmonic — how many times higher is the frequency, and how many nodes are there?
Two-source interference
Two sources vibrating in phase send out waves of the same wavelength λ. Where the path difference Δr = |r₁ − r₂| is a whole number of wavelengths, the waves add up (bright fringe); where Δr is an odd multiple of λ/2, they cancel (dark fringe). The colour shows the intensity I = cos²(πΔr/λ).
Try this: Move the sources further apart and watch the number of fringes grow. Then drag point P onto a dark fringe and read Δr/λ.
Frequently asked questions
What is Oscillations & Waves?
Oscillations & Waves is a free interactive simulation from StudyFi Lab. It runs right in your browser, with no sign-up and nothing to install. Pendulums, springs, waves and interference
Is Oscillations & Waves free?
Yes. Oscillations & Waves is completely free. It works in the browser on computers, tablets and phones, and you do not need an account.
What can I explore in Oscillations & Waves?
Simple pendulum, Mass on a spring, Travelling wave, Standing wave on a string, Two-source interference.
What does the “Simple pendulum” experiment show?
A bob on a string of length L swings under gravity according to θ″ = −(g/L)·sin θ. For small angles T = 2π√(L/g), and the period does not depend on the amplitude. At large angles the actual period is longer. Energy flows between kinetic and potential, while the total stays the same.
What does the “Mass on a spring” experiment show?
A spring of stiffness k pulls a mass m back to equilibrium, and the damping b slows it: x″ = −(k/m)·x − (b/m)·x′. Without damping it oscillates with T = 2π√(m/k). At b = 2√(km) (critical damping) it returns fastest without overshooting; with larger b it creeps back more slowly. Damping gradually removes energy.
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