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Point Mass Analysis
Point Mass Analysis
Definition of point mass oscillation time T in seconds (s), where:
r = distance between the rotation point and location of Center of Gravity (CoG) of the point mass representation of the pendulum clock.
g = gravitational acceleration.
It can be noted that:
Only the distance r is needed for this calculation!
r and g must use the same length units to ensure T has the units of seconds.
if g = 9.81 m/s^2, then r must be expressed in meters (m) too.
Calculations:
Natural Frequency in radians/sec: 12.003 radians/sec
Natural Frequency in Hz: 1.910 Hz
Calculated Time of One Revolution of Escapement Wheel: 7.328 sec
Calculated Period of Oscillation: 0.523 sec
Measured Time of Period of Oscillation: ~0.64 sec
Percent Error: 22.37%
Inertial Analysis
Inertial Analysis
Definition of inertial oscillation time T in seconds (s), where:
I_tot is the total inertia of the pendulum clock around the rotation point, including the pendulum body and the possible n screws/bolts included in your pendulum.
The value of I_tot is computed as the sum of two main components:
The inertial effect of the pendulum body as the pendulum body mass m times the squared distance r between the rotation point and location of Center of Gravity (CoG) of the pendulum body
The inertial effect of the possible n screws/bolts as the screw/bolt mass m_k times the squared distance r_k between the rotation point and location of Center of Gravity (CoG) of each screw/bolt
m_r is the distance weighted mass of the pendulum clock around the rotation point, including the pendulum body and the possible n screws/bolts included in your pendulum.
The value of m_r is also computed as the sum of two main components:
The distance weighted mass of the pendulum body as the pendulum body mass m times the distance r between the rotation point and location of Center of Gravity (CoG) of the pendulum body.
The distance weighted mass of the possible n screws/bolts as the screw/bolt mass m_k times the distance r_k between the rotation point and location of Center of Gravity (CoG) of each screw/bolt
It can be noted that:
Both pendulum mass m, possible screws/bolt masses m_k and their respective distances r and r_k of the CoGs to the rotation point are required for calculations!
If there are no screws/bolts (n = 0), it can be observed that the formula for T simplifies back to the point mass analysis, where only the value of r is needed!
r, r_k and g must use the same length units to ensure T has the units of seconds.
if g = 9.81 m/s^2, then r and r_k must be expressed in meters (m) too.
Calculations:
Total Moment of Inertia: 0.605 grams m^2
Natural Frequency in radians/sec: 9.529 radians/sec
Natural Frequency in Hz: 1.517 Hz
Calculated Time of One Revolution of Escapement Wheel: 9.231 sec
Calculated Period of Oscillation: 0.659 sec
Measured Time of Period of Oscillation: ~0.64 sec
Percent of Error: 2.94%
Two-dimensional Simulation Analysis
Two-dimensional Simulation Analysis
WM2D Simulation Analysis
WM2D Simulation Analysis
Period: 0.55 sec
Period: 0.55 sec
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