Case 1
- Mass
- 0.5kg
- Spring constant
- 200N/m
0.314159s
Open with these valuesSpring Mass Period Calculator
0.314159s
Result: 0.314159 sA mass on a spring oscillates with T = 2π√(m ÷ k): heavier is slower, stiffer is faster. A 0.5 kg mass on a 200 N/m spring completes one oscillation in 0.314159 s. Gravity does not appear — the same spring and mass keep time identically on the Moon.
Worked examples
Case 2
- Mass
- 1kg
- Spring constant
- 1N/m
6.283185s
Open with these valuesCase 3
- Mass
- 2kg
- Spring constant
- 8N/m
3.141593s
Open with these valuesHow it's calculated
T = 2π × √(m ÷ k)
- StepEnter the mass in kilograms — grams divided by 1000.
- StepEnter the spring constant in newtons per metre.
- ResultDivide mass by spring constant, take the square root, multiply by 2π.
Reference table
| Mass (kg), spring constant (N/m) | Note | Period (s) |
|---|---|---|
| 0.25, 100 | Light mass, medium spring | 0.314159 |
| 0.5, 200 | Both doubled — the same period | 0.314159 |
| 1, 1 | The unit case: the period is 2π | 6.283185 |
| 2, 8 | Ratio one to four: the period is π | 3.141593 |
| 4, 16 | Same ratio, same period | 3.141593 |
Questions
How do I calculate the period of a mass on a spring?
Use T = 2π × √(m ÷ k), where m is the mass in kilograms and k is the spring constant in newtons per metre. A 0.5 kg mass on a 200 N/m spring gives T = 2π × √(0.5 ÷ 200) ≈ 0.314159 s.
What is the spring constant?
The spring constant k measures a spring's stiffness — the force in newtons needed to stretch or compress it by one metre. It comes from Hooke's law, F = kx. A larger k means a stiffer spring, which pulls the mass back harder and gives a shorter period.
How does the mass affect the period?
Heavier masses oscillate more slowly. Because the mass sits under a square root, the period grows with the square root of m: quadrupling the mass only doubles the period. A 2 kg mass swings twice as slowly as a 0.5 kg mass on the same spring, not four times.
Does the swing distance change the period?
No. For an ideal spring obeying Hooke's law the period depends only on the mass and the spring constant, not on how far you pull the mass. That is the defining feature of simple harmonic motion, as long as the spring is not stretched past its elastic limit.
Does gravity change the answer?
No — and this is where the spring differs from the pendulum. Gravity shifts where the mass hangs at rest, but the restoring force around that point still comes only from the spring. The same spring and mass keep the same period on the Moon.
What units should I use?
SI units: kilograms for the mass and newtons per metre for the spring constant, which gives the period in seconds. If your mass is in grams, divide by 1000 before entering it.
Sources and last check
Information, not professional advice.