SLIDE 1
Origin of simple harmonic motion Old Slide U(x) = ½ kx2 Total energy Total energy
kx
- F=
Class 15: Calculation of natural frequency Class 15: Calculation of - - PowerPoint PPT Presentation
Class 15: Calculation of natural frequency Class 15: Calculation of - - PowerPoint PPT Presentation
Class 15: Calculation of natural frequency Class 15: Calculation of natural frequency Old Slide Origin of simple harmonic motion U(x) = kx 2 Total energy Total energy F = - kx x V=0 a is max V=0, a is max. V=0 a is max V=0, a is max. a=0, v
SLIDE 2
SLIDE 3
Arbitrary potential Arbitrary potential Taylor expansion of arbitrary potential about x=x :
L ) x
- x
)( (x U" 1 ) x
- x
)( (x U' ) U(x U(x)
2
+ + + =
Taylor expansion of arbitrary potential about x=x0:
) )( ( 2 ) )( ( ) ( ( )
F i l h i i For simple harmonic motion, U(x0) ‐‐‐ Irrelevant, just an offset U’( ) 0 Si l h i i U’(x0)=0 ‐‐‐ Simple harmonic motion always occur at the i i t ti l minimum potential
SLIDE 4
Simple harmonic motion of arbitrary potential Given arbitrary potential U(x) Suppose U(x )=0
) x x )( (x U" 1 ) U(x U(x)
2
+
Given arbitrary potential U(x). Suppose U(x0)=0
) x
- x