Question

This is simple harmonic lab with this setup

Photogate - Metal tab 000000000 Glider

• 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

selleles

Consider a mass m with a spring on either end, each attached to a wall. Let and be the spring constants of the springs. A displacement of the mass by a distance x results in the first spring lengthening by a distance x (and pulling in the direction), while the second spring is compressed by a distance x (and pushes in the same direction). The equation of motion then becomes

$m\ddot{x}=-k_{1}x-k_{2}x=-\left ( k_{1}+k_{2} \right )x$

so the effective spring constant of the system is k₁ + k₂, and the time period of the oscillation will be

$T=2\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$

The time period depends on the mass and spring constants. If it is not leveled perfectly, the time period will not change much. But, if there is some inclination due to non leveling of the air track, there will be different displacement affected by the weight components on the spring ends.