Final answer:
The frequency of the oscillation of a 99.0 cm long pendulum is approximately 0.282 Hz, calculated using the formula T = 2π√(l/g), where T is the period of the pendulum, l is the length of the pendulum, and g is the acceleration due to gravity.
Step-by-step explanation:
To determine the frequency of the oscillation of a pendulum that is 99.0 cm long, we can use the formula for the period of a simple pendulum:
T = 2π√(l/g)
where:
- T is the period of the pendulum (the time it takes to complete one full oscillation)
- l is the length of the pendulum (99.0 cm or 0.99 m in this case)
- g is the acceleration due to gravity (approximately 9.81 m/s² on the surface of the Earth)
Plugging in the values, we get:
T = 2π√(0.99 m / 9.81 m/s²)
T ≈ 2π√(0.1009 s²)
T ≈ 2π√(0.3174 s)
T ≈ 6.2832√(0.3174 s)
T ≈ 6.2832 × 0.5634 s
T ≈ 3.54 s
Once we have the period, we can find the frequency by taking the reciprocal of the period:
f = 1/T
f ≈ 1/3.54 s
f ≈ 0.282 Hz
Therefore, the frequency of the oscillation of the pendulum is approximately 0.282 Hz.