Practice

T = 2π√(m/k) Formula – SHM Practice

T = 2π√(m/k) — Mass-spring SHM period

For a mass on a spring, the period is T = 2π√(m/k). Ideal SHM period does not depend on amplitude.

Guide — how to use this formula

1. 1. T = 2π√(m/k); convert g → kg if needed.
2. 2. k = 4π²m/T²; m = k(T/2π)².
3. 3. Amplitude does not change T.
4. 4. f = 1/T; energy at max stretch uses ½kA².

Derivation

From a = −(k/m)x with angular frequency ω = √(k/m):

1. Period:
   T = 2\pi\sqrt{\frac{m}{k}}
2. Solve for k:
   k = \frac{4\pi^{2} m}{T^{2}}

Don’t confuse with the pendulum T = 2π√(L/g).

Examples

Example: m = 1, k = 4

T = π ≈ 3.14 s.

Example: double mass

T multiplies by √2.

Practice on the interactive page

Calculator · All practice formulas