A pendulum has a mass of 2.7 kg, a length of 1.7 meters, and swings through a (half)arc of 22.7 degrees. What is its amplitude to the nearest centimeter?

Well, normally we measure amplitude of a pendulum in degrees, so the amplitude written this way would be

Theta=22.7*Cos(2PI*t/Period)
and amplitude is 22.7 deg.

Now with all the data you gave, and asking for amplitude in cm, then measured from the center of mass, the ARC length measurement is 1.7*2PI*22.7/360 and some would call that amplitude.

To find the amplitude of the pendulum, we need to understand what amplitude means in the context of a pendulum. The amplitude is the maximum displacement of the pendulum bob from its equilibrium position.

Here's how you can calculate the amplitude of the pendulum:

1. Convert the angle from degrees to radians. Since the formula for amplitude involves the angle in radians, we need to convert 22.7 degrees to radians. We can do this by multiplying the angle in degrees by the conversion factor π/180.

Angle in radians = 22.7 degrees * (π/180)
Angle in radians ≈ 0.396 radians

2. Use the formula for the amplitude of a pendulum. The formula for the amplitude of a pendulum is given by:

Amplitude = Length * sin(angle)

Given that the length of the pendulum is 1.7 meters and the angle in radians is 0.396, we can substitute these values into the formula.

Amplitude = 1.7 meters * sin(0.396)
Amplitude ≈ 1.617 meters

3. Convert the amplitude to the nearest centimeter. Since the answer is required to the nearest centimeter, we can convert the amplitude from meters to centimeters by multiplying it by 100.

Amplitude ≈ 1.617 meters * 100 cm/meter
Amplitude ≈ 161.7 centimeters

Therefore, the amplitude of the pendulum to the nearest centimeter is approximately 161.7 centimeters.