Time Period Of Spring Mass System — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Time Period of Spring-Mass System Valid for ideal simple harmonic motion where the spring mass is negligible compared to the attached mass, and the elastic limit is not exceeded. Start with Newton's Second Law: F = ma Substitute Hooke's Law for restoring force: -kx = ma Rearrange to differential form: a + (k/m)x = 0 Compare with standard SHM equation: a + (omega 2)x = 0 Identify angular frequency: omega = sqrt(k/m) Use relation T = 2 pi / omega Mass (m) must be > 0 Spring constant (k) must be > 0 Damping forces (friction/air resistance) are negligible Spring mass is negligible Believing the time period depends on the amplitude of oscillation (it does not for SHM). Assuming the length of the spring directly appears in the period formula (it affects k, but isn't explicitly in the T formula). Confusing frequency (f) with angular frequency (omega) or period (T).