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January 26, 2015

January 26, 2015

Posted by **katie** on Friday, May 11, 2007 at 5:07pm.

The head of an industrial machine moves in a straight line horizontally backwards and forwards from a central position. The movement can be modelled using the sine wave d = 80 sin ( pie t), where d is the horizontal distance (in cm) from the central starting position, and t is the time after the machine starts running (in second).

choose two statements which are true about the motion of the machine.

1)the maximum distance that the machine head moves horizontally from its central starting position is 80 cm.

2) The maximum distance that the machine head moves horizontally from its central starting position is 40 cm.

3) The machine head will make 50 complete cycles in a minute.

4) The machine head will make 30 complete cycles in a minute.

5) The machine head will make one complete cycle in half a minute.

6) The machine head will make one complete cycle in two minutes.

the largest value for sine of any angle is +1, which when multiplied by 80 gives a maximum value of 80, so 1) is true

the period of sin(kx) is 2pi/k

so the period of 80sin(pi t) = 2pi/pi = 2

since t was defined as seconds the machine will complete one complete cycle in 2 seconds.

So which answer would fit that conclusion?

Bob, I think it's #4,

It takes 2 seconds to complete one cycle, which is 30 cycles per minute.

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