An asymmetrical double torsion pendulum for studying coupled harmonic motion

Taking the upper inertia member, for example, the ratio between the moments of inertia of the shaft collar and the disc with respect to the axis of rotation is $[18ms(ϕ12+ϕ22)]/(12maR2)≈4.7×10−5$⁠. For a guitar wire of about $1 m$ in length, which is longer than any section of the guitar wire used in the asymmetrical DTP, its mass was measured to be $m=0.41 g$⁠, and thus, the ratio of the moment of inertia of the guitar wire with respect to the rotation axis to that of the disc is $(12mr2)/(12maR2)≈1.7×10−8$⁠.

$I=12(ma+mb/2)R2≈2.42×10−4 kg m2$⁠. The uncertainty of $I$ mainly results from the mass and thus is evaluated by $12(ma−mb/2)R2≈0.02×10−4 kg m2$⁠.

To set the wire lengths, we used a segment of a measuring tape of $0.1 cm$ in precision. Thus, the uncertainty of every wire length is estimated to be $0.2 cm$⁠. For simplicity, this uncertainty is not presented in the value of any wire length.

The raw rotation angles of the STP are fitted with $θ′(t)=θ0+C sin (ωt+φ)$⁠. The rotation angle $θ(t)$ is obtained by subtracting θ₀ from $θ′(t)$⁠.

The raw rotation angles of the asymmetrical DTP are fitted with $θb′(t)=θ0+θ+ sin (ω+t+φ+)+θ− sin (ω−t+φ−)$⁠. The rotation angle $θb(t)$ is obtained by subtracting θ₀ from $θb′(t)$⁠.