ww As shown in Figure QC2. the 25-kg square plate is pinned at comer A and attac

Question

ww

As shown in Figure QC2. the 25-kg square plate is pinned at comer A and attached to a spring having a stiffness of k - 300 N/m. as in the figure below. If the plate is released from rest when theta = 0 degree. determine its angular velocity when theta = 90 degree. The spring is unstretched when theta = 0 degree. Note: For a thin plane, the mass moment of inertia about an axis perpendicular to the plate's plane and passing through the center of mass is Izz=1/2m(a2+b2), where a and b are the side lengths of the plate.

Explanation / Answer

mg*0.3/2=1/2*Iw^2+1/2*kx^2

at theta we have length of spring =0.3sin(45+theta)/sin((135-theta)/2)

So at theta =0 L=0.23 and at theta=90 L=0.55

So x=0.32433 m(more precisely)

So

36.75=15.7785+0.5*(0.5m(a^2+b^2)+m(a^2+b^2)/4)w^2=15.7785+1.6875w^2

So w=3.5253 rad/s

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