Dynamic Analysis

Point Mass Analysis

The equation for point mass analysis is 2π√(r/g), where "r" is the distance from the pivot point to the center of mass and g is the acceleration of gravity (9.8 m/s2 ).

I measured the "r" by balancing the pendulum on my fingertip to find the center of gravity, then measured the distance with a ruler. (Result: 7cm).

When I plugged the numbers into the equation, 2π√(0.07/9.8), I got a period of 0.531 seconds.

Inertial Analysis

The equation for inertial analysis is 2π√(Itotal / mr g), where "Itotal " is the total inertia of the pendulum plus the bolts. and "mr g" is the mass-radius of each object times the acceleration of gravity.

Equation for Itotal : mbody r2body + m1 r21 + m2 r22

Equation for mr : mbody rbody + m1 r1 + m2 r2

Subscript "body" is the acrylic body of the pendulum, and "1" and "2" are bolts placed on the pendulum.

I measured the masses with a electronic scale and got the "r" of each object using Fusion 360.

Mass of body: 0.074kg "r" of body: 0.062m Inertia of body: 0.0002845 mr of body: 0.004588

Mass of bolt 1: 0.00794kg "r" of bolt 1: 0.146m Inertia of bolt 1: 0.0001692 mr of bolt 1: 0.001159

Mass of bolt 2: 0.00397kg "r" of bolt 2: 0.150m Inertia of bolt 2: 0.00089302 mr of bolt 2: 0.000595

Itotal : 0.000543 mr total: 0.006342

2π√(0.000543 / 0.006342*98) = 0.5873 seconds

Two-dimensional Simulation Analysis

Include a video with graphs produced by WM2D to predict what the oscillation frequency or oscillation time is of your clock based on a simulation of your clock pendulum.

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