Question:

A simple pendulum consists of a mass of 0.2 kg attached to a string of length 0.5 m. If the pendulum is displaced by an angle of 10 degrees and released from rest, what is its period of oscillation? (Assume no air resistance)

Solution:

The period of oscillation of a simple pendulum is given by the formula:

T = 2π√(L/g),

where L is the length of the string and g is the acceleration due to gravity (approximately 9.81 m/s^2).

First, we need to convert the angle of displacement from degrees to radians:

θ = 10 degrees = 10 * π/180 radians ≈ 0.1745 radians

Next, we can use the small angle approximation sin(θ) ≈ θ to simplify the formula for the period of oscillation:

T = 2π√(L/g) ≈ 2π√(θ/g)

Substituting the values into the formula, we get:

T = 2π√(θ/g) = 2π√(0.1745/9.81) ≈ 0.72 seconds

Therefore, the period of oscillation of the simple pendulum is approximately 0.72 seconds.

(ref: chat.openai.com)