Periodic motion and the simple-harmonic condition

Over what mass and amplitude range does T = 2π√(m/k) predict a real spring oscillator's period, and what does the residual pattern reveal? Useful evidence includes period data across masses and amplitudes, a linearized T²-versus-m fit, an intercept converted to the spring's effective mass and compared with the predicted one third of the spring's own mass, residuals, and a stated range of validity.

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. Third-semester content is the least standardised of the introductory sequence: departments place oscillations, waves, optics, and thermal physics differently, and the modern-physics units here are a bounded survey rather than a complete course in relativity, quantum mechanics, atomic, nuclear, or particle physics. Follow your institution's published scope, notation, laboratory programme, and assessment rules. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.