Find the position of a pendulum as a function of time?

In summary, the position of a pendulum can be found as a function of time using the equation f(t) = Acos(ωt), where A is the amplitude and ω is the angular frequency. In this case, the amplitude is 0.35m and the angular frequency is 1.81t, which can be calculated using the period equation T = 2π√(l/g). The displacement of the pendulum is represented by the amplitude, and the angle of displacement is represented by the angular frequency.
  • #1
Camphi
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0

Homework Statement


How do you find the position of a pendulum as a function of time?

Mass of bob: 2.0kg
String length (l): 3.0m

The pendulum is displaced as a distance of 0.35m from the equilibrium point and is then released. After 100 swings the maximum displacement of the pendulum has been reduced to 0.15m.

Homework Equations


[/B]
Period (T) of a pendulum: T = 2π√(l/g)

The Attempt at a Solution


The answer to the problem is f(t) = 0.35cos(1.81t) but I am not understanding how the 0.35 or the 1.81t is coming into play because I figured that if the angle is the point where the equilibrium point and the place where the pendulum is attached to a wall then the 0.35 would be opposite of this angle, not the adjacent of hypotenuse of the triangle created from the displacement of the pendulum. I also figured that the 0.35 was what the displacement was and I do not understand where the 1.81 came from at all.
 
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  • #2
I have had an epiphany so moderators can lock this thread.
 

Related to Find the position of a pendulum as a function of time?

1. How does the length of the pendulum affect its position as a function of time?

The length of the pendulum does not affect the position of the pendulum as a function of time. The only factors that affect the position of a pendulum are its initial angle and the force of gravity.

2. How can we calculate the position of a pendulum at a specific time?

The position of a pendulum at a specific time can be calculated using the equation: x = A*cos(ωt), where x is the position, A is the amplitude (initial angle), ω is the angular frequency, and t is the time.

3. Can the position of a pendulum be negative?

Yes, the position of a pendulum can be negative. This occurs when the pendulum swings to the left of its equilibrium point. The position is considered positive when the pendulum swings to the right of its equilibrium point.

4. How does the weight of the pendulum affect its position?

The weight of the pendulum does not affect its position as a function of time. However, it does affect the period of the pendulum, which is the time it takes for one full swing. A heavier weight will result in a longer period.

5. Can the position of a pendulum be affected by air resistance?

Yes, air resistance can affect the position of a pendulum, but it is usually negligible. In an ideal scenario, where there is no air resistance, the position of a pendulum would follow a perfect sinusoidal curve. However, in real-world scenarios, air resistance can cause a slight decrease in amplitude and an increase in the period of the pendulum.

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