Conical Pendulum (10, 3)

Equations:

g

h = L ⋅ COS(θ )

2 ⋅ π

ω = --

T = ----------

h

 

ω

 

ω = 2 ⋅ π ⋅ f

 

Example:

Given: L=25_cm, h=20_cm.

Solution: θ=36.899_°, T= 0.8973_s, ω=7.0024 r/s, f=1.1145_Hz.

Torsional Pendulum (10, 4)

Equations:

w =

G---------⋅J-

T =

2----------⋅ π

ω = 2 ⋅ π ⋅ f

 

L ⋅ I

 

ω

 

Example:

Given: G=1000_kPa, J=17_mm^4, L=26_cm, I=50_kg∗m^2.

Solution: ω=1.1435E°–3_r/s, f=1.8200E–4_Hz, T=5494.4862_s.

Simple Harmonic (10, 5)

Equations:

x = xm ⋅ COS( ω ⋅ t +φ)

v = –ω ⋅ xm ⋅ SIN(ω ⋅ t + φ )

a = –ω2⋅ xm ⋅ COS(ω ⋅ t + φ )

ω = 2 ⋅ π ⋅ f

5-42 Equation Reference