Question

PLEASE HELP I ONLY HAVE 12 MINUTES!! The pendulum of the grandfather clock shown below swings at a maximum angle of 25 degrees. The arc length of the path of a full pendulum swing measures 1/2n feet. How long, in feet, is the pendulum?

Answer 1

Answer: T = 2π√(I/mgD)

Explanation:

where:

m is the mass of the pendulum;

I is the moment of inertia of the mass; and

D is the distance from the center of mass to the point of suspension.

Determine the length of the pendulum. For example, it can be equal to 2 m.

Decide a value for the acceleration of gravity. We will use the Earthly figure of 9.80665 m/s², but feel free to check how the pendulum would behave on other planets.

Calculate the period of oscillations according to the formula above: T = 2π√(L/g) = 2π * √(2/9.80665) = 2.837 s.

Find the frequency as the reciprocal of the period: f = 1/T = 0.352 Hz.

You can also let this simple pendulum calculator perform all calculations for you!