Final answer:
When the length of a pendulum increases, the natural frequency of the pendulum decreases.
Step-by-step explanation:
When the length of a pendulum increases, the natural frequency of the pendulum decreases.
we find the cooling constant. Once we have k, we can write the complete model for the temperature of the coffee as a function of time, t, in minutes.
The natural frequency of a simple pendulum is given by the formula:
f = 1 / (2π √(l / g))
where f is the frequency, l is the length of the pendulum, and g is the acceleration due to gravity.
Since the natural frequency is inversely proportional to the square root of the length, if the length of the pendulum increases by a factor of 4, the frequency will decrease by a factor of 2.