- #1
dannyR
- 5
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hello everyone, I've completed a experiment regarding torsional oscillations to determin the tortional ridgity in two types of wire. The final result is about what is to be expected but I am having trouble in calculating the error in my C " torsional ridigity" value.
The formula used is [2Pi^2M(R^2+r^2)]/(t2^2-t1^2)=C
the experiment was done by a torquing a disk of mass M connected to the end of the wire where R is the outer radius and r is the inner radius of the disc t2,t1 are the average times of the oscillations t1 being one mass and t2 being 2 masses this is to eliminate the unknown moment of inertia of the connecting bolt used to connect the disc to the end of the wires.
so to calculate the error in c when R,r,M,t1and t2 all have small errors due to measurments either reading errors or stdevp/N^0.5 in the case of the T the periods.
i have been calculating the error in MR^2 then Mr^2 using
(dM/M)^2+2(dR/R)^2=(dmR^2/mR^2)^2=(dx/x)^2, (dx/x) for simplicity x=mR^2
(dM/M)^2+2(dr/r)^2=(dmr^2/mr^2)^2=(dy/y)^2
then to add these two errors would i get:
using dQ^2=dx^2+dy^2=x^2[(dM/M)^2+2(dR/R)^2]+y^2[(dM/M)^2+2(dr/r)^2],
where dQ would be the total error in the top line of the fraction of the formula
the bit I am unsure about is when changing (dx/x)^2 to just dx^2 let's say (dx/x)^2=Z would the dx^2 to be =x^2*Z
can someone please comment if i am corrrect so far and if not please point me in the right direction as I am adament to get this correct as it is vital i learn to do this for myself.
Thanks a lot just for reading. Dan:)
The formula used is [2Pi^2M(R^2+r^2)]/(t2^2-t1^2)=C
the experiment was done by a torquing a disk of mass M connected to the end of the wire where R is the outer radius and r is the inner radius of the disc t2,t1 are the average times of the oscillations t1 being one mass and t2 being 2 masses this is to eliminate the unknown moment of inertia of the connecting bolt used to connect the disc to the end of the wires.
so to calculate the error in c when R,r,M,t1and t2 all have small errors due to measurments either reading errors or stdevp/N^0.5 in the case of the T the periods.
i have been calculating the error in MR^2 then Mr^2 using
(dM/M)^2+2(dR/R)^2=(dmR^2/mR^2)^2=(dx/x)^2, (dx/x) for simplicity x=mR^2
(dM/M)^2+2(dr/r)^2=(dmr^2/mr^2)^2=(dy/y)^2
then to add these two errors would i get:
using dQ^2=dx^2+dy^2=x^2[(dM/M)^2+2(dR/R)^2]+y^2[(dM/M)^2+2(dr/r)^2],
where dQ would be the total error in the top line of the fraction of the formula
the bit I am unsure about is when changing (dx/x)^2 to just dx^2 let's say (dx/x)^2=Z would the dx^2 to be =x^2*Z
can someone please comment if i am corrrect so far and if not please point me in the right direction as I am adament to get this correct as it is vital i learn to do this for myself.
Thanks a lot just for reading. Dan:)