1.565872597159 radian Using the supplied information and any appropriate assumptions and / or approximations to determine the following; 1) the mass moment of inertia I 2) the natural angular frequency ωn 3) the initial angular displacement θ
Consider a flat rectangular plate of known mass, width and breadth with a negligible thickness that lies in the horizontal xy-plane. The plate is suspended from a thin piece of piano wire that is in the vertical orientation coincident to the z-axis and where the piano wire is attached to the center of the plate. When the plate is subjected to a torque whose vector is coincident to the z-axis, the plate rotates in the horizontal plane such that the rotation of the plate is modelled as θ=Csin(ωnt+ϕ).
The parameter information is:
mass of plate M = 1.2 kilogram
width of plate W = 0.040 meter
breadth of plate B = 0.075 meter
shear modulus of piano wire G = 79.3 gigaPascals
diameter of piano wire D = 0.003 meter
length of piano wire L = 0.120 meter
amplitude of rotation C = 0.087267520415 radian
phase lag of rotation ϕ = 1.565872597159 radian
Using the supplied information and any appropriate assumptions and / or approximations to determine the following;
1) the mass moment of inertia I
2) the natural angular frequency ωn
3) the initial
4) the initial
5) extra points: plot the solution for θ(t) for a small time interval
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