Poll Question

1
Poll Question

• The period of a spring simple harmonic oscillator
  depends on
• (Add together the numbers for all correct choices
  and text in the sum.)
• 1. The spring constant k.
• 2. The mass m.
• 4. The maximum amplitude A.
• 8. The gravitational field g.

2
Pendulums

• almost follow Hookes law

14.414.6
3
Angular Oscillators

• Angular Hookes law
• t kq
• Angular Newtons second law
• t Ia
• So
• kq Ia
• General Solution
• q Q cos(wt f)
• where w2 k/I Q and f are constants

4
Simple Pendulum

• Massless, inextensible string/rod
• Point-mass bob

5
Poll Question

• The period of a simple pendulum depends on
• (Add together the numbers for all correct choices
  and enter the sum.)
• 1. The length L.
• 2. The mass m.
• 4. The maximum amplitude Q.
• 8. The gravitational field g.

6
Simple Pendulum Force

• SFT wT mg sinq

7
Simple Pendulum Torque

• SFT wT mg sinq
• LFT L mg sinq
• Restoring torque

8
Small-Angle Approximation

• For small q (in radians)
• q ? sin q ? tan q

9
Simple Pendulum

• t L mg sinq
• t ? L mg q kq
• k Lmg
• I mL2

w2 k/I
g/L
w is independent of mass m
(w is not the angular speed of the pendulum)
10
Board Work

• Find the length of a simple pendulum whose period
  is 2 s.

About how long is the pendulum of a grandfather
clock?
11
Think Question

• An extended object with its center of mass a
  distance L from the pivot, has a moment of
  inertia
• greater than
• the same as
• less than
• a point mass a distance L from the pivot.

12
Poll Question

• If a pendulum is an extended object with its
  center of mass a distance L from the pivot, its
  period is
• longer than
• the same as
• shorter than
• The period of a simple pendulum of length L.

13
Physical Pendulum
Source Young and Freedman, Figure 13.23.
14
Physical Pendulum
Fnet mg sinq tnet mgd sinq Approximately
Hookes law t ? mgdq
I Icm md 2
15
Example Suspended Rod

• Mass M, center of mass at L/2

harder to turn
easier to turn
16
Physical Pendulum

• What is the period when d gtgt R?