Final answer:
The period of oscillation for the pendulum with a length of 0.75 m and mass of 0.5 kg, released from a 22-degree angle to the vertical, is approximately 1.73 seconds.
Step-by-step explanation:
The question asks for the period of oscillation of an ideal simple pendulum, which has a length (ℓ) of 0.75 meters and supports a mass (m) of 0.5 kilograms. The pendulum makes an angle of 22 degrees with respect to the vertical. The formula for the period (T) of a simple pendulum is T = 2π√(ℓ/g), where ℓ is the length of the pendulum and g is the acceleration due to gravity, which is approximately 9.8 m/s². As the amplitude of the pendulum's swing is less than 15°, we can use this formula to calculate the period.
Plugging in the given values, the period of oscillation is: T = 2π√(0.75 m / 9.8 m/s²). Therefore, T is approximately 1.73 seconds.