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

In summary, the conversation discusses the problem of finding the vertical displacement of a pendulum at a specific time, given its length and a sine function that models its angle of displacement. The participants discuss their attempts at solving the problem, including finding the angle and using trigonometry to calculate the time. They also note that there can be multiple solutions due to the periodic nature of the function. However, one participant points out that the given equation does not have a variable to solve for time and suggests using Pythagoras theorem and inverse trigonometric functions to find the desired time.
  • #1
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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?

?
:(
 
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  • #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.
 

1. How do you find the vertical displacement of a pendulum in 4 seconds?

To find the vertical displacement of a pendulum in 4 seconds, you will need to use the equation: d = (L * sinθ) - (L * cosθ), where d is the displacement, L is the length of the pendulum, and θ is the angle of displacement. You can also use a calculator or trigonometric tables to find the sine and cosine values.

2. What is the formula for finding the vertical displacement of a pendulum?

The formula for finding the vertical displacement of a pendulum is d = (L * sinθ) - (L * cosθ), where d is the displacement, L is the length of the pendulum, and θ is the angle of displacement.

3. Can you explain the concept of vertical displacement?

Vertical displacement is the distance between the starting point and the ending point of an object's vertical motion. In the case of a pendulum, it is the vertical distance between the highest and lowest points of its swing.

4. Why is it important to find the vertical displacement of a pendulum?

Finding the vertical displacement of a pendulum allows us to determine the amplitude of its swing, which is an important factor in understanding its motion and predicting its behavior. It also helps us calculate the potential energy and kinetic energy of the pendulum at different points in its swing.

5. What other factors can affect the vertical displacement of a pendulum?

The length of the pendulum, the angle of displacement, and the initial velocity can all affect the vertical displacement of a pendulum. Other external factors such as air resistance and friction may also have a small impact on the displacement.

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