What is the acceleration acting on a grandfather clock's pendulum, of length 0.9m, with a maximum angular displacement of 0.1rad?
What is the total distance traveled by that pendulum in one complete oscillation?
Show your work for further assistance
To find the acceleration acting on a grandfather clock's pendulum, we can use the formula for the acceleration of an object in simple harmonic motion:
a = (ω^2) * x
Where:
a is the acceleration
ω is the angular frequency
x is the displacement
First, we need to find the angular frequency (ω). The formula for angular frequency is:
ω = 2πf
Where:
ω is the angular frequency
f is the frequency of oscillation
Since a grandfather clock typically swings back and forth in a time period of 2 seconds, the frequency (f) is 1/2 Hz.
Substituting the value of frequency into the formula:
ω = 2π * (1/2) = π rad/s
Now we know the angular frequency (ω), the displacement (x), and can calculate the acceleration (a):
a = (π^2) * (0.1) = 0.31 m/s^2
So, the acceleration acting on the grandfather clock's pendulum is 0.31 m/s^2.
To find the total distance traveled by the pendulum in one complete oscillation, we can use the formula:
total distance = 2π * length
Where:
total distance is the distance traveled in one complete oscillation
length is the length of the pendulum
Substituting the given length:
total distance = 2π * 0.9 = 5.65 meters
Therefore, the total distance traveled by the grandfather clock's pendulum in one complete oscillation is 5.65 meters.