To find the angular frequency of the motion, we can use the formula:
ω = √(g/L)
where:
- ω is the angular frequency in radians per second,
- g is the acceleration due to gravity (approximately 9.8 m/s²), and
- L is the length of the pendulum.
1. Substitute the given values into the formula:
ω = √(9.8 / 0.79)
2. Calculate the square root and divide:
ω = √(12.405¹²⁵ / 0.623²⁵) ≈ √19.8614 ≈ 4.46 rad/s
The angular frequency of the motion is approximately 4.46 radians per second.
To find Bob's speed as it passes through the lowest point of the pendulum swing, we can use the formula for velocity in simple harmonic motion:
v = ω * A
where:
- v is the velocity,
- ω is the angular frequency, and
- A is the amplitude of the oscillation.
In this case, the amplitude is the distance from the equilibrium position to the maximum displacement, which is equal to the length of the pendulum (0.79 m).
3. Substitute the values into the formula:
v = 4.46 * 0.79
4. Multiply to find the velocity:
v ≈ 3.52 m/s
Bob's speed as it passes through the lowest point of the pendulum swing is approximately 3.52 meters per second.