# Simple Harmonic Motion: Crash Course Physics #16

TLDRThis video explores oscillations and simple harmonic motion, using the example of London's Millennium Bridge. It explains how the bridge's unexpected swaying was caused by resonance that amplified small oscillations. The physics of simple harmonic motion is illustrated through a ball on a spring. Using uniform circular motion, equations are derived for properties like period, frequency, and angular velocity. Finally, it's shown that the position graph of an object in simple harmonic motion is a wave, relating back to the bridge's wave-like motion.

###### Takeaways

- π The swaying of the Millennium Bridge was caused by oscillations, specifically simple harmonic motion
- π Simple harmonic motion involves back-and-forth oscillations that follow a consistent pattern
- π‘ The total energy of an oscillating object transforms between kinetic and potential energy
- π There are equations that describe the velocity, period, frequency and angular velocity of simple harmonic motion
- π Simple harmonic motion is mathematically similar to uniform circular motion
- πΈ Resonance can increase the amplitude of an oscillation by applying force at the right frequency
- π The Millennium Bridge engineers didn't account for horizontal swaying caused by people walking
- π€ Engineers fixed the bridge by applying forces to counteract its oscillations
- π The position graph of an object in simple harmonic motion looks like a wave
- π Simple harmonic motion helps explain concepts like waves that are covered in later episodes

###### Q & A

### What caused the Millennium Bridge in London to sway back and forth dramatically when it first opened?

-The swaying of the Millennium Bridge was caused by oscillations resulting from the force of people's footsteps as they walked across it. This set the bridge into simple harmonic motion.

### How did the pedestrians walking on the bridge make the swaying worse?

-As the bridge began swaying, pedestrians started leaning into the motion to keep their balance. This had the effect of applying force at the same frequency as the bridge's oscillations, amplifying its motion through resonance.

### What are the two main forms of energy at play in simple harmonic motion?

-The two main forms of energy in simple harmonic motion are kinetic energy (energy of motion) and potential energy stored in the spring or other elastic medium.

### What is the relationship between simple harmonic motion and uniform circular motion?

-Simple harmonic motion exhibits many of the same mathematical properties as uniform circular motion. Looking at circular motion from the side makes the similarities clear.

### What equation relates the position of an oscillating object to time?

-The equation x = A cos wt relates the position (x) of an oscillating object to time (t), where A is the amplitude and w is the angular velocity.

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

-Resonance is when an external force is applied at the natural frequency of an oscillating system, greatly increasing its motion. People walking on the bridge applied resonant forces that amplified its swaying.

### What changes did engineers make to fix the excessive swaying of the Millennium Bridge?

-Engineers applied fixes that counteracted the bridge's oscillations, preventing resonant forces from amplifying its horizontal sway.

### What is the period of a mass on a spring in simple harmonic motion?

-The period of simple harmonic motion is T = 2Οβ(m/k), where m is the oscillating mass and k is the spring constant.

### What is the maximum velocity of a mass on a spring?

-The maximum velocity is vmax = A(k/m)1/2, where A is the amplitude, k is the spring constant, and m is the mass.

### Why did the engineers not anticipate the horizontal swaying of the bridge?

-The engineers only accounted for vertical oscillations in their design. They didn't realize people walking would induce side-to-side swaying as well.

###### Outlines

##### π€ How the Millennium Bridge's oscillations reveal connections to physics concepts

This paragraph discusses the opening of London's Millennium Bridge in 2001 and how its horizontal swaying motion had to be closed almost immediately. It outlines how the bridge took on an S-shape and resembled a wave. The problem was caused by oscillations resulting from resonance of people's footsteps. This physics concept connects to ideas about simple harmonic motion.

##### π Relating simple harmonic motion to uniform circular motion using math

This paragraph makes a comparison between simple harmonic motion (a ball on a spring) and uniform circular motion (a marble moving around a ring), showing how their motion graphs when viewed from the side are similar. It then uses concepts of circular motion like period, frequency and angular velocity to derive equations that can describe the motion of the spring ball over time.

###### Mindmap

###### Keywords

##### π‘Oscillations

##### π‘Simple harmonic motion

##### π‘Resonance

##### π‘Potential energy

##### π‘Kinetic energy

##### π‘Amplitude

##### π‘Period

##### π‘Frequency

##### π‘Angular velocity

##### π‘Waves

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###### Transcripts

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