Question

A simple pendulum with mass m = 1.7 kg and length L = 2.38 m hangs from the ceiling. It is pulled back to an small angle of θ = 11.5° from the vertical and released at t = 0.

1)
What is the period of oscillation?

Answer 1

The period of oscillation for a simple pendulum with a length of 2.38 m is approximately 3.10 seconds, using the formula T = 2π √(L/g).

Step-by-step explanation:

The simple pendulum under discussion has a mass (m) of 1.7 kg and a length (L) of 2.38 m. Since the pendulum's amplitude (θ) is less than 15°, we can approximate its period of oscillation using the formula for simple harmonic motion (SHM): T = 2π √(L/g), where g is the acceleration due to gravity (approximately 9.81 m/s² on the surface of the Earth).

To calculate the period, we apply the formula:
T = 2π √(2.38 m / 9.81 m/s²)
T ≈ 2π √(0.2427 s²)
T ≈ 2π √(0.2427) s
T ≈ 2π × 0.4927 s
T ≈ 3.0964 s

Therefore, the pendulum's period of oscillation is approximately 3.10 seconds.