The maximum magnitude of velocity and acceleration of a simple pendulum can be determined based on its period and amplitude.
- Maximum Magnitude of Velocity (Vmax): The maximum magnitude of velocity occurs when the pendulum is at its equilibrium position (lowest point) and changes direction. At this point, all the potential energy is converted to kinetic energy.
To find Vmax, we can use the equation: Vmax = amplitude * angular frequency
The angular frequency (ω) can be calculated using the formula: ω = 2π / T
where T is the period of the pendulum.
Given: Period (T) = 2.0 s Amplitude = 5.0 cm = 0.05 m
First, calculate the angular frequency: ω = 2π / T = 2π / 2.0 s = π rad/s
Then, calculate Vmax: Vmax = amplitude * angular frequency = 0.05 m * π rad/s ≈ 0.157 m/s
Therefore, the maximum magnitude of velocity of the pendulum bob is approximately 0.157 m/s.
- Maximum Magnitude of Acceleration (amax): The maximum magnitude of acceleration occurs when the pendulum is at its maximum displacement from the equilibrium position (highest point). At this point, the acceleration is solely due to the force of gravity and can be calculated using the formula:
amax = g * amplitude
where g is the acceleration due to gravity (approximately 9.8 m/s²).
Given: Amplitude = 5.0 cm = 0.05 m
Calculate amax: amax = g * amplitude = 9.8 m/s² * 0.05 m = 0.49 m/s²
Therefore, the maximum magnitude of acceleration of the pendulum bob is 0.49 m/s².