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 the 2 correct statements about the motion of the machine:
a) the maximum distance that the machine head moves horizontally from its central starting position is 80cm
b) the maximum distance that the machine head moves horizontally from its central starting position is 40 cm
c) the machine head will make 50 complete cycles in a minute
d) the machine head will make 30 complete cycles in a minute
e) the machine head will make one complete cycle in half a minute
f) the machine head will make one complete cycle in 2 minutes.
I'm assuming its A and E. Anybody have a better idea if I'm wrong?
I agree with you, but show me your thinking for E.
Sure! To determine if statement E is correct, we need to find the time it takes for the machine head to complete one full cycle.
The equation given for the motion of the machine head is d = 80 sin(πt), where d is the horizontal distance in cm and t is the time in seconds. In one complete cycle, the sine function goes from its minimum value to its maximum value and then back to its minimum value.
The sine function has a period of 2π, which means it completes one full cycle every 2π seconds. In this case, we have a value of π (pi) as the argument of the sine function, so we can infer that one complete cycle is completed in 2 seconds.
Since there are 60 seconds in a minute, the machine head will make one complete cycle in half a minute, which supports statement E. Therefore, your initial assumption that the correct statements are A and E is indeed correct.