SOLUTION: A pendulum is connected to a rope 3 m long, which is connected to a ceiling 4 m high. The angle between its widest swing and vertical hanging position is π/3. If the pendulum swin

Question 1205131: A pendulum is connected to a rope 3 m long, which is connected to a ceiling 4 m high. The angle between its widest swing and vertical hanging position is π/3. If the pendulum swings out to its widest position in 2 seconds, model the horizontal displacement of the pendulum using a sinusoidal function, considering vertical to be x = 0.

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
a rope long
a ceiling high

so, from the floor to the pendulum is => minimum height
the vertical distance to the ceiling is :

since the highest angle is just and , the smallest distance to the ceiling is

and
the highest point is from the ground

then, cosine function will be:

range of the pendulum's height above the ground is
, where

amplitude is
midline is
the period is =>
and, function is:

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