Consider a flat rectangular plate of mass M = 0.743 kilogram, width W = 0.048 meter, and breadth B = 0.078 meter with a

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Consider a flat rectangular plate of mass M = 0.743
kilogram, width W = 0.048 meter, and breadth B =
0.078 meter with a negligible thickness t that lies in the
horizontal xy-plane. The plate is suspended from
a thin piece of piano wire with a shear modulus of G =
77979741026 pascals and diameter D = 0.003 meter and
length L = 0.118 meter such that the wire is in a vertical
orientation that is coincident with the z-axis, and the
plate rotates by an angle θ in the horizontal plane.
Measurements reveal that the angle may be modelled as
θ=0.09sin(ωnt+1.67541) where
the angle θ is in radians and the phase lag ϕ
is in radians.
It is desired to calculate the moment of inertia I
, the torsional spring constant kt, the
natural angular frequency ωn, the plate initial
rotational displacement θ0, and the plate initial
rotational velocity θ˙0
.
For the supplied information determine:
b) the piano wire torsional spring constant
kt
/ [N.m/rad] to 4 significant figures