Physics- SHM and Phasors.?

Question

I was given this example but I dont understand how to get the answers, the answers are given below each question.

Thanks in advance, any help is really appreciated!

Please follow the link to the question as I couldn't write it all in here so I uploaded it as an image file.
http://img76.imageshack.us/img76/773/shmth6.jpg

Answer 1

ok, it's postion as a function of time, the derivative is velocity as a function of time. the derivative is
v(t) = 20 x -sin(4.4t+pi/7.0) x 4.4
first question is 'max speed'. there is some point where the sine function of t = 1, so max speed at that point is 20 x 1 x 4.4 = 88

earliest time for equilibrium is when position equation = 0 so
20 x cos (4.4t+pi/7.0) = 0, solve for t
cos (4.4t+pi/7.0) = 0
Arccos of 0 = pi/2 so
4.4t+pi/7.0 = pi/2
t = (pi/2 - pi/7.0)/4.4 = 0.255

extremity position occurs when the cos of the freq function = 1
Cos (4.4t+pi/7.0) = 1
solve for t as in above solution

for the energy the KE = 1/2mv^2. so ratio of energy is ratio of Mb x Vmax / Mc x Vmaxc
Vmax of C is a function of the amplitude 31. as in first sample it works out to 31x1x4.4=136.4. so ratio =
(136.4^2 x 363g)/(88^2x106g) = 8.23

phase diff should be intuitive, and phase constant is plug and chug

Answer 2

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