Answer Happy

= = Consider a flat rectangular plate of mass M = 0.642 kilogram, width W = 0.038 meter , and breadth B = 0.073 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 = 74115584937 pascals and diameter D = 0.002 meter and length L = 0.092 meter such that the wire is in a vertical orientation that is coincident with the k-axis, and the plate rotates by an angle in the horizontal plane. Measurements reveal that the angle may be modelled as Ô = 0.092 sin wat + 1.695171) where the angle 0 is in radians and the phase lag o is in radians. = - It is desired to calculate the moment of inertia I, the torsional spring constant kt. the natural angular frequency wn, the plate initial rotational displacement Co, and the plate initial rotational velocity .. For the supplied information determine: e) the plate initial rotational velocity 00 / [rad/s] to 4 significant figures