|Nov16-10, 02:26 PM||#1|
trig word problem
1. The problem statement, all variables and given/known data
A pedulum, which is 0.5 m long, swings back and forth. The angle of it's displacement from it's original position is modelled by:
Theta = 1/4Sin(Pi/3)
IN the first 4 seconds, when will the vertical displacement of the pendulum be 1 cm?
3. The attempt at a solution
What I did was:
Find the angle theta.
The pendulum can swing to the left into an imaginary "Quadrant 3" so
sin theta = 0.01/0.5
theta = _____
Then I subbed that into the equation and got a decimal answer.
I was sure there was more than one answer, so in the last minute, I added Pi and _____, since it's in the third quadrant. And ended up with 3. something.
The other class did this question the day before our test and ended up with 4 answers!
I looked at the solutions, but one of them was 5.94 or along those lines, but it didn't satisfy what the question was looking for - the first 4 seconds
That teacher also drew the 1 cm displacement on the horizontal component of the pendulum, which was odd... didn't it ask for the vertical?
|Nov22-10, 12:04 PM||#2|
First off there will always be more than one answer when dealing with periodic functions like sine and cosine. This is why they said in the first 4 seconds! Indacating your answer should be 4 seconds or less.
I don't think your equation is right, because it means theta = a constant, because there is no variable in your equation. Is there meant to be a t in there somewhere?
I worked out theta to be 88.85 (degrees) to make the vertical displacement 1 cm. I did this by drawing the diagram, using Pythagoras theorem to find the horizontal displacement then using atan(O/A) = theta. Without a variable in the equation you gave the time cannot be calculated.
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