FIND......................
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According to the question, the deflected beam is in the shape of the parabola
x² = 4ay
and (0,0) is the point of maximum deflection.As deflection in the center is 9cm, y co-ordinate of the points of support is +9. Assuming the beam is symmetrically loaded and geometrically symetric about its center, x co-ordinates of the support points are -6 and 6.Hence (-6,9) and (6,9) lie on the beam and satisfy the given parabola.
So, 6² = 4a*9
or 36 = 36a
or a = 1
Thus the equation becomes
x² = 4y ...........(1)
Now deflection of the required points is 5cm. Therefore their y co-ordinate is 9-5 = 4
Putting this value of y in equation (1),we get
x² = 4*4
or x = ±4
Therefore (-4,4) , (4,4) are the points on the beam with deflection 5 cm.
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