Question

Simple Harmonic Motion.

Background The period of an object oscillating on the end of a spring is given by the formula: 1 IM T= 2011 "V k (1) Here, the spring constant k comes from the usual definition by Hooke's law, in terms of the force of the spring at some displacement from the equilibrium position x 1 : F = -k(x – xo) (2) If we let M denote the mass of the object oscillating, this accurately describes an ideal situation in which springs are massless. There is actually a correction 2 when we consider the case of springs whose mass is not negligible. If we let MG be the mass of the things oscillating (the glider, potentially plus more) and Ms be the mass of the springs, then the effective mass M (which we plug into the above formula) is defined by: M = MG + Ms/3 We will also make use of the potential energy stored in a spring: 1 J = 5k(x – Xo)2 Note that the total kinetic energy also uses the same effective mass M in place of the mass of the glider.

Effective Spring Constant: In Part I you measured the k_effective of the two springs acting together. If the two springs had k₁ and k₂ individually, how would they combine to get k_eff?

• Systemic Error: Leveling Air Track: We level the air track in this lab because it's good lab procedure in general, but in fact in this lab a not-level (but still straight) air track shouldn't change any of our results. Explain why this is true (for each part).²

Answer 1

Sotn: K2 Since, both spring co eapeicnte sorme dorteF d Hookels las F- K, de sping F- K22 de sing 2) coher and x2 is deforrmahun o Sproing and 2 c) To lal dfomahon yikm 2F KI 42 -1-2pdo -F() Sints, F K KI 12 5 lora 1 F KeJ Comparny esn ) and) 부부 -부