Simple Harmonic Motion: Crash Course Physics #16

Summary

In June 2001, the Millennium Bridge in London had to be closed almost immediately after opening due to severe swaying caused by pedestrians' footsteps. This swaying was a result of oscillations and resonance, a phenomenon where force applied at the right frequency increases amplitude. Engineers initially overlooked horizontal swaying, leading to dangerous resonance. By analyzing simple harmonic motion and comparing it to uniform circular motion, we understand the bridge's issues. Ultimately, engineers implemented solutions to counteract the oscillations, stabilizing the bridge. This video explains these concepts in detail, using the Millennium Bridge as a real-life example.

Takeaways

• 🌉 The Millennium Bridge in London was closed soon after opening due to swaying caused by the force of pedestrians' footsteps, illustrating the physics of oscillations.
• 🔁 Simple harmonic motion is a type of oscillation that follows a consistent pattern, often described using the example of a ball attached to a spring.
• 🏋️‍♂️ Kinetic and potential energy are key in understanding oscillations; kinetic energy is maximum at the equilibrium point, while potential energy is highest at the amplitude.
• 📈 The maximum velocity of an oscillating object can be calculated using the formula involving amplitude, spring constant, and mass.
• ⏱ The period, frequency, and angular velocity of simple harmonic motion can be understood by drawing parallels with uniform circular motion.
• 📐 The position of an object in simple harmonic motion over time can be described using trigonometry, specifically the cosine function.
• 🔄 The graph of an object's position versus time in simple harmonic motion resembles a wave, which helps explain the wave-like motion of the Millennium Bridge.
• 🤸‍♀️ Resonance, the phenomenon where an oscillation's amplitude is increased by applying force at the right frequency, played a significant role in the bridge's swaying.
• 👷‍♂️ Engineers had to redesign the Millennium Bridge to counteract the oscillations, focusing on the horizontal swaying that was initially overlooked.
• 🔍 The script emphasizes the importance of considering all aspects of oscillation, including both vertical and horizontal movements, in engineering designs.
• 🎓 The episode provides a comprehensive lesson on simple harmonic motion, connecting it with concepts from uniform circular motion and demonstrating its real-world applications.

Q & A

What was the main issue with the Millennium Bridge when it first opened?

The main issue with the Millennium Bridge was that it swayed back and forth dramatically due to the force of pedestrians' footsteps, leading to severe oscillations.

How did pedestrians' actions worsen the swaying of the Millennium Bridge?

Pedestrians leaned into the swaying to keep from falling over, which created resonance and amplified the oscillations.

What is simple harmonic motion?

Simple harmonic motion is a type of oscillation where the motion follows a consistent, repeating pattern, such as a ball attached to a spring moving back and forth.

What happens to the energy of a ball in simple harmonic motion as it moves?

As the ball moves, its kinetic energy increases towards the middle of its motion while its potential energy decreases, keeping the total energy constant.

How is the maximum velocity of a ball in simple harmonic motion determined?

The maximum velocity is determined by the equation: maximum velocity = amplitude * sqrt(spring constant / mass).

What similarities exist between simple harmonic motion and uniform circular motion?

Mathematically, simple harmonic motion is similar to uniform circular motion. For example, if a marble moves in a circular path, its horizontal motion can be seen as analogous to the back-and-forth motion of a ball on a spring.

How do you calculate the period of a ball in simple harmonic motion?

The period is calculated as: period = 2 * pi * sqrt(mass / spring constant).

What is resonance and how did it affect the Millennium Bridge?

Resonance is the increase in amplitude of an oscillation by applying force at the right frequency. On the Millennium Bridge, pedestrians created resonance by leaning into the swaying, worsening the oscillations.

Why did the engineers not foresee the swaying issue of the Millennium Bridge?

The engineers did not foresee the swaying issue because they only considered vertical oscillations, not the horizontal swaying caused by pedestrians walking.

What measures were taken to fix the Millennium Bridge?

Engineers applied a series of changes to the bridge to counteract its oscillations and prevent it from swaying dramatically.