Period vs Mass

For spring-mass SHM: T = 2π·√(m/k). Period proportional to √m.

Doubling mass increases T by √2 (~1.41×).

T² vs m gives a straight line through origin — slope = 4π²/k. Lab method to measure k.

For a SIMPLE PENDULUM: T does NOT depend on mass — period depends only on L and g.

Why difference? Spring force scales with displacement (not mass), so heavier mass takes longer to accelerate. Pendulum gravity scales with mass (= weight), so mass cancels out.

In rotational systems, 'mass' is replaced by moment of inertia I.

Same principle: increasing inertia at constant restoring force/torque ⇒ slower oscillation.

Useful for designing tuning forks, accelerometers, mechanical clocks.