The period of a simple pendulum is given by the formula:
T = 2π √(L/g),
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, the period of the pendulum is given as 2 seconds. We can rearrange the formula to solve for L:
L = (gT^2) / (4π^2).
Let's assume the acceleration due to gravity, g, is approximately 9.8 m/s^2. Converting the amplitude from centimeters to meters, we have:
Amplitude (A) = 5 cm = 0.05 m.
The angular velocity (ω) can be calculated using the formula:
ω = 2π / T.
Substituting the given period, we get:
ω = 2π / 2 = π rad/s.
The frequency (f) of the pendulum can be calculated as the reciprocal of the period:
f = 1 / T = 1 / 2 = 0.5 Hz.
Therefore, the angular velocity of the pendulum is π rad/s, and its frequency is 0.5 Hz.