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Time period of a mass on a spring calculator

A-level Oscillations

The time for one oscillation of a mass on a spring, which does not depend on the amplitude.

T = 2π√(m / k)

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

0.497 s

Working

  1. Write the equation
    T = 2π√(m / k)
  2. Substitute the values
    T = 2π × √(0.25 ÷ 40)
  3. Calculate
    T = 0.496729 s
  4. Give the answer to 3 significant figures
    T = 0.497 s

Worked example

Find T, the time period. Given: mass m = 0.250 kg; spring constant k = 40.0 N/m.

  1. Write the equation
    T = 2π√(m / k)
  2. Substitute the values
    T = 2π × √(0.25 ÷ 40)
  3. Calculate
    T = 0.496729 s
  4. Give the answer to 3 significant figures
    T = 0.497 s

Symbols and units

SymbolQuantitySI unit
TTime periods
mMasskg
kSpring constantN/m

Time period of a mass on a spring: rearranged

  • To find time period: T = 2π√(m / k)
  • To find mass: m = k T2 / (4π2)
  • To find spring constant: k = 4π2 m / T2

Exam tip

A stiffer spring (larger k) gives a shorter period. A larger mass gives a longer period.

Common questions

What is the formula for time period of a mass on a spring?

The equation is T = 2π√(m / k), where T is the time period (s); m is the mass (kg); k is the spring constant (N/m).

What units should I use for time period of a mass on a spring?

In SI units: time period in s, mass in kg, spring constant in N/m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange T = 2π√(m / k)?

Rearranging gives these forms: to find time period: T = 2π√(m / k). to find mass: m = k T² / (4π²). to find spring constant: k = 4π² m / T².

Practise time period of a mass on a spring questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Related

Read the full explanation on the Period of a mass on a spring formula page. More oscillations equations: Time period of a simple pendulum, Maximum speed in simple harmonic motion, Maximum acceleration in simple harmonic motion. See the full list on the a-level physics equation calculator page.