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

[Camphi]

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

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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.

 

[Camphi]

I have had an epiphany so moderators can lock this thread.