- #1
discoverer02
- 138
- 1
I think I'm lost in the ugly algebra, but I want to make sure.
A uniform rectangular plate is suspended at point P (top center of the rectangle), and swings in the plane of the paper about an axis through P. At what other point between P and O (center of the rectangle), along PO, could the plate be suspended to have the same period of oscillation as it has around P. O is the cm of the plate.
The rectangle has a width and b length.
The answer is (a^2b)/(3(a^2 + b^2))
T = period.
I = moment of inertia
M = mass
1) T = 2pi(I/mgd)^(1/2) I = (1/12)M(a^2 + b^2) + M(b/2)^2
d = b/2
2) T = 2pi[(8b^2 + 2a^2)/(12mgb)]^(1/2)
I then substitute (b/2 - x) for d in equation 1 and set it equal to equation 2 and solve for x, but I'm not getting the correct answer. Is this the correct approach?
Thanks.
The perpetually confused discoverer02.
A uniform rectangular plate is suspended at point P (top center of the rectangle), and swings in the plane of the paper about an axis through P. At what other point between P and O (center of the rectangle), along PO, could the plate be suspended to have the same period of oscillation as it has around P. O is the cm of the plate.
The rectangle has a width and b length.
The answer is (a^2b)/(3(a^2 + b^2))
T = period.
I = moment of inertia
M = mass
1) T = 2pi(I/mgd)^(1/2) I = (1/12)M(a^2 + b^2) + M(b/2)^2
d = b/2
2) T = 2pi[(8b^2 + 2a^2)/(12mgb)]^(1/2)
I then substitute (b/2 - x) for d in equation 1 and set it equal to equation 2 and solve for x, but I'm not getting the correct answer. Is this the correct approach?
Thanks.
The perpetually confused discoverer02.