PHY C13: Energy in Oscillations

Today we’re covering:

  • Types of Energy
    • Kinetic
    • Potential
  • Total Energy

Let’s go!


What types of energy exist in Simple Harmonic Motion?

Kinetic energy Definition Energy due to motion
(change in displacement x over time t)
Kinetic Energy
at any point x
Ek = ½ mv2

Since v = ω√(x02 – x2),
½ m[ω√(x02 – x2)]2

Ek = ½ mω2(x02x2)

Maximum Kinetic Energy
(when v = maximum, v0)
½ mv02

OR

½ mω2x02

Graph of Ek against Displacement (x) Screenshot 2019-05-04 at 11.14.12 PM.png
Graph of Ek against Time (t) Screenshot 2019-05-04 at 11.21.38 PM.png
Potential energy

 

Definition Work done AGAINST restoring force
(motion is always OPPOSITE direction of Fres)Consists of:

  • Gravitational Potential Energy
  • Elastic Potential Energy (for springs)
Potential Energy
at any point x
Ep = ½ mω2x2

 

Because:
Fres = – mω2x

W = FΔx,
Ep = FΔx

Since Fres varies, we need to find the AVERAGE F to plug into the formula:
F = ½Fres

Thus,
Ep = ½Fresx2
(the negative disappears since it shows the direction of Fres, & Ep is a scalar)

Maximum Potential Energy
(when a = maximum, x = maximum, x0)
½mω2x02
Graph of Ep against Displacement (x) Screenshot 2019-05-04 at 11.26.19 PM.png
Graph of Ep against Time (t) Screenshot 2019-05-04 at 11.21.47 PM.png

 


How do these values change?
Remember: in Free Oscillations & thus Simple Harmonic Motion, there is NO ENERGY LOSS.

TOTAL energy (Kinetic + Potential) = CONSTANT

Screenshot 2019-05-04 at 11.15.01 PM.png
Both types of energy against displacement

 

Screenshot 2019-05-04 at 11.24.09 PM.png
Both types of energy against time

Therefore,

Maximum Kinetic Energy = Maximum Potential Energy

(You can check in the table above: they have the same formula in fact!)

Etot = Ek + Ep
Etot = ½ mω2(x02 – x2) + ½ mω2x2
Etot = ½ mω2x02

 OR

Etot = Ekmax = Epmax
Etot = ½ mω2x02


⇐ Previous in Physics: Simple Harmonic Motion
⇒ Next in Physics: Damped Oscillations

One thought on “PHY C13: Energy in Oscillations

  1. Pingback: PHY C13: Damped Oscillations – ProDuckThieves

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s