a thin horizontal rod

[monokekie]

A thin horizontal rod, OA, 2 metres long, is fixed horizontally to a wall at O and a wight is hung at the other end, A, causing it to bend. The downward deflection, y, of a point x metres from O satisfies the equation: f''(x)=0.024(2-x). Given that the deflection of the beam and its inclination to the horizontal are both zero at O, find the deflection at the middle of the rod


any hint would be highly appreciated!

[kamil9876]

I'm assuming you mean f(x)=y.

antidifferentiate and use 0=f(0)=f'(0). Inclination to horizontal means something along the lines 'angle from horizontal' but probably in terms of gradient rather than angle, anyway in either case it implies f'(0)=0

[monokekie]

thank you very much Kamil9876!
um.. i am pretty sure it is a second derivative..

i am just wondering..
how do we find the position of the middle of the rod?

[kamil9876]

Lol technically you need arclength formula, is this in the spec course? I think it's not. Though maybe x=1 (half of 2m) can be used as an approximation

[monokekie]

i subed in x=1 and it worked !!! tkx ter tao!LOL