Floating cylinder oscillating in a liquid: SHM from buoyancy
Push a floating cylinder down and let go. The buoyant force acts as a restoring force and the cylinder performs SHM with T = 2π√(h/g). Change the density of the cylinder, its length and the liquid and check the time period.
Also searched as: floating body oscillation · floating body oscillation · shm of a floating cylinder · time period of floating cylinder · simple harmonic motion examples · oscillation of a floating body
About this experiment
| Subject | Physics |
|---|---|
| Class | 11 |
| Chapter | 13. Oscillations |
| NCERT section | 13.4–13.6 |
| Level | NCERT level |
| Time | about 15 minutes |
| Access | Included in a PractiSci plan |
Aim
To show that a cylinder floating upright in a liquid performs simple harmonic motion when pushed down, and to find its time period.
Theory
At rest the weight of the cylinder is balanced by the buoyant force: ρc A L g = ρl A h g, so the length under water is h = L ρc / ρl. If the cylinder is pushed down by x, an extra length x goes under water and the buoyant force increases by ρl A x g. This extra force acts upwards, towards the equilibrium position, and is proportional to x: F = −(ρl A g) x. That is the condition for SHM with force constant k = ρl A g.
The mass is m = ρc A L, so ω = √(k/m) = √(ρl g / (ρc L)) and T = 2π √(ρc L / (ρl g)) = 2π √(h / g). The time period depends only on the length h under water. It does not depend on the area of the cross-section or on the amplitude (as long as the cylinder stays partly out of the water).
The same idea gives the period of a hydrometer, of a ball in a U-tube of liquid and of a floating buoy. If the liquid is viscous, energy is lost and the amplitude decays (damped oscillation).
Formulas used
- h = L ρc / ρl (length under water)
- restoring force F = − ρl A g x, k = ρl A g
- ω = √(ρl g / (ρc L)), T = 2π √(h / g)
- x(t) = A cos ωt
Procedure: what to do in the virtual lab
- Set the cylinder density to 600, the liquid to 1000 and the length to 30 cm. Check that h = 18 cm and T = 0.85 s.
- Change the length of the cylinder. How does T change?
- Change the density of the liquid: does a denser liquid make the oscillation faster or slower?
- Increase the amplitude: does T change?
- Add damping and watch the amplitude fall.
Observations to make
- The measured motion lies on the cosine curve of the theory.
- T depends on the submerged length h only.
- A denser liquid gives a smaller h, a shorter period.
What you can change in this experiment
- Density of the cylinder (200 to 900 kg/m³)
- Density of the liquid (800 to 1400 kg/m³)
- Length of the cylinder (10 to 60 cm)
- Push down by (0 to 10 cm)
- Viscous damping
Viva questions on Floating cylinder oscillating in a liquid
Questions an examiner may ask in the Class 11 physics practical. Run the experiment in the lab to find the answers yourself, then check them in the Learn tab.
- Why is the motion of a floating cylinder simple harmonic?
- On what quantities does the time period depend?
- What is the length under water if the density of the cylinder is half that of the liquid?
- Does the area of the cross-section affect the period?
Frequently asked questions
What is the aim of the Floating cylinder oscillating in a liquid experiment?
To show that a cylinder floating upright in a liquid performs simple harmonic motion when pushed down, and to find its time period.
Which formulas are used in the Floating cylinder oscillating in a liquid experiment?
h = L ρc / ρl (length under water); restoring force F = − ρl A g x, k = ρl A g; ω = √(ρl g / (ρc L)), T = 2π √(h / g); x(t) = A cos ωt
What viva questions are asked on Floating cylinder oscillating in a liquid?
Why is the motion of a floating cylinder simple harmonic? On what quantities does the time period depend? What is the length under water if the density of the cylinder is half that of the liquid? Does the area of the cross-section affect the period?
How do I do the floating body oscillation experiment for Class 11 online?
Open the Floating cylinder oscillating in a liquid virtual lab on PractiSci, follow the procedure above, change the values and read the live graph. It matches the Class 11 physics practical, with the aim, theory, observations and viva questions on this page.
What is the time period of a floating cylinder?
T = 2π √(h / g), where h = L ρc / ρl is the length immersed at equilibrium. It does not depend on the amplitude.
Why is the motion of a floating cylinder simple harmonic?
Pushed down by x, the extra buoyant force is ρl A g x upwards. A restoring force proportional to the displacement gives SHM.
What happens to the period if the liquid is denser?
The immersed length h = L ρc / ρl becomes smaller, so the time period becomes shorter.
Can I do the Floating cylinder oscillating in a liquid experiment online?
Yes. Open it as a 3D virtual lab in your browser or on your phone, change the values and read the results from live graphs. It is part of a PractiSci plan.
Syllabus: Class XI Physics, Chapter 13 — Oscillations, §13.5 (simple harmonic motion), §13.6 (restoring force examples)
What you do in the lab
Change the controls and watch the physics behave in real time in 3D. Live readouts and graphs show the numbers behind it, and the Learn tab has the theory, procedure, observations and viva questions. Works on a phone or a laptop, in English and Hindi.
Topics: simple harmonic motion · floating body · buoyancy · time period · restoring force · oscillations · Archimedes
Read the full guide: Oscillations and waves.
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