Mass-spring period does not depend on amplitude

The mistake

Assuming a larger oscillation must take longer because it travels farther.

Why it feels right

More distance usually means more time.

How to catch it

You put amplitude A into T = 2π √(m/k) for an ideal spring.

The first principle

For ideal SHM, larger amplitude also gives larger maximum speed. The period T = 2π √(m/k) is independent of amplitude.

worked mini-example

A spring oscillator's amplitude doubles. What happens to its period?

Common wrong move

It doubles.

Correct

It stays the same in the ideal SHM model.

Test the repair SHM-04 · transfer

The amplitude of an ideal mass-spring oscillator is tripled without changing m or k. Its period:

Triples Increases by √3 Stays the same Becomes one-third

Make a fresh prediction before referring to the worked example.