Chapter 15 Oscillation

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Chapter 15 : Oscillations

Motions that Repeat themselves

Chapter 15 : Oscillations

Motions that Repeat themselves

Chapter 15 : Oscillations

Motions that Repeat themselves

Motion repeats, but it’s a bit discontinuous / jumpy. It’s not smooth.

Chapter 15 : Oscillations

We limit ourselves to motion that is repetitive but

also “simple”

Here, simple essentially means that the object’s position varies as a sine

wave.

Chapter 15 : Oscillations

We have a couple examples of simple harmonic

oscillators:

When is the velocity largest? Acceleration?

https://www.youtube.com/watch?v=yVkdfJ9PkRQ

Simple harmonic motion

Sine wave

repeats

7

Simple harmonic motion

Sine wave

repeats

How do we describe this motion?

How large is it? What is the amplitude of motion?

How long does it take to repeat? What’s its period?

What’s its frequency?

How fast does it move? When is it fastest? Slowest?

What about acceleration?

8

Why “Simple Harmonic motion (SHM)”?

x(t) = x max cos(ωt + ϕ )

dx

v(t) =

= −x max ω sin (ωt + ϕ )

dt

€ a(t) = dv = −x ω 2 cos(ωt + ϕ )

max

dt

Position

Velocity

Acceleration

[v

max

= x max ω ]

a max = x max ω 2 ]

[

€

Magnitude of velocity is maximized when the position is 0.

Magnitude of acceleration is maximized when the position is also.

€

a(t) = −ω 2 x(t)

In SHM, the acceleration is proportional to the displacement but opposite

sign. The proportionality is the square of the angular frequency.

€

SHO...