Library / Foundations: Physics / FPH-20
Foundations: Physics
Period of a mass on a spring
Time for one oscillation of a mass on a spring.
- Ref
- FPH-20
- Rev
- v1
- Field
- Foundations: Physics
- Result
- T [s]
Light spring and negligible damping. m in kg, k in N/m, T in s.
Heavier masses oscillate more slowly; stiffer springs oscillate faster.
Calculator
s
kg
N/m
- Frequency3.183 Hz
- Angular frequency20 rad/s
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
Period (s) current value 0.3142 s
mMassKey driver
0.04444.44
kSpring constant
0.04444.44
- The period does not depend on the amplitude (for small oscillations).
- Quadrupling the mass doubles the period.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| m Mass | 0.01 to 100 kg | 0.04443 | 4.443 | 4.398 | +10% | +4.88 % |
| k Spring constant | 1 to 10,000 N/m | 0.04443 | 4.443 | 4.398 | +10% | −4.65 % |
Sweep of Mass
| Mass (kg) | Period (s) |
|---|---|
| 0.01 | 0.04443 |
| 0.03162 | 0.07901 |
| 0.1 | 0.1405 |
| 0.3162 | 0.2498 |
| 1 | 0.4443 |
| 3.162 | 0.7901 |
| 10 | 1.405 |
| 31.62 | 2.498 |
| 100 | 4.443 |
Sweep one variable
Period (s)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
T
Period
What the equation gives you. Everything else feeds it.
m
Mass
Oscillating mass. Raises the period with the square root.
k
Spring constant
Spring stiffness. Lowers the period with the square root.
Worked example with the values above
- m/k = 0.5 / 200 = 0.0025.
- Square root: 0.05.
- T = 2π × 0.05 = 0.3142 s.
Assumptions and limits
- Light spring, no damping.
- Hooke’s law holds.
Common mistakes
- Using the spring mass as well as the load without correction.
- Forgetting the 2π.
Statistics and uncertainty
Timing 10 oscillations and dividing by 10 reduces the timing error on T by ten.
Where it is used
- Instrument and equipment mounts.
- Suspension design.
Maths you need
- Hooke’s law: F = kx
- Square roots: √(m/k)