Embedded Files
Timing Analysis Sheet
Timing Analysis Sheet
This spreadsheet was used to calculate the total mass and center of mass of our clock pendulum system, including added bolts and nuts. We first determined the mass and volume of the acrylic pendulum arm, then compared the calculated and actual mass to find the percent error.
Physics Calculations
Physics Calculations
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.
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.
Page updated
Report abuse