10. A wrecking ball attached to a crane may be thought of as a pendulum. The period of such a pendulum is given (in seconds) by P = 4k (from 0 to /2) of (dx/ 1-a sin x)) where a = sin( /2, is the angle of the swing (measured in radians from the rest position), k = r/g), r is the length of the cable holding the ball, and g is the acceleration due to gravity. Suppose the construction engineer determines that a period of P = 5 seconds is required for wrecking ball to have its maximum impact, and suppose that k = .75. Using a symbolic calculator, compute the angle required for the swing as follows: Since the integral cannot be computed exactly, approximate the integrand by its fifth-degree (teacher said might be 4th degree) Taylor polynomial at x = 0. Then integrate, solve the equation for a, and compute from a.
our hints were:
1 - has to do with a tough derivative and cosine
2 - f(0) = 1
I tried to do it on the 89 and I got .961451 after about 3 minutes of it processing. :)
2007-02-19 04:15:58 · 1 answers · asked by bobby_b 1 in Science & Mathematics ➔ Mathematics
10. A wrecking ball attached to a crane may be thought of as a pendulum. The period of such a pendulum is given (in seconds) by P = 4k [integral](from 0 to [pi]/2) of (dx/[sqrt]1-a[squared]sin[squared]x)) where a = sin([theta]/2, [theta] is the angle of the swing (measured in radians from the rest position), k = [sqrt]r/g), r is the length of the cable holding the ball, and g is the acceleration due to gravity. Suppose the construction engineer determines that a period of P = 5 seconds is required for wrecking ball to have its maximum impact, and suppose that k = .75. Using a symbolic calculator, compute the angle [theta] required for the swing as follows: Since the integral cannot be computed exactly, approximate the integrand by its fifth-degree (teacher said might be 4th degree) Taylor polynomial at x = 0. Then integrate, solve the equation for a, and compute [theta] from a.
our hints were:
1 - has to do with a tough derivative and cosine
2 - f(0) = 1
2007-02-19 05:27:57 · update #1
That's a crack. I'm trying but can u pls re-type/modify the following lines? particularly the angles
"...P = 4k (from 0 to /2) of (dx/ 1-a sin x)) where a = sin( /2, is the angle of the swing (measured in radians from the rest position), k = r/g), r..."
I'm still stuck...i guess i'll hve to watch for a solution...I got the intergral though:
[arcsin.(a.sin(a))] from 0 to pi/2
2007-02-19 04:50:08 · answer #1 · answered by raqandre 3 · 0⤊ 0⤋