Trig Word Problem: Finding Vertical Displacement of a Pendulum in 4 Seconds

[Vee9]

Homework Statement

A pedulum, which is 0.5 m long, swings back and forth. The angle of it's displacement from it's original position is modeled by:
Theta = 1/4Sin(Pi/3)

IN the first 4 seconds, when will the vertical displacement of the pendulum be 1 cm?

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?

?
:(

 

[madmike159]

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.