1. SCI 340 L27 Simple Pendulum
Question
The period of a simple harmonic oscillator depends on: A. The spring constant k. B. The mass m. C. The maximum amplitude A. D. The gravitational field g.

2. SCI 340 L27 Simple Pendulum almost follow Hooke’s law
Pendulums
almost follow Hooke’s law
§ 10.4

3. Torsional Oscillator Angular Hooke’s law: t = –kq
SCI 340 L27 Simple Pendulum
Torsional Oscillator
Angular Hooke’s law:
t = –kq
Angular Newton’s 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 L q m Massless, inextensible string/rod Point-mass bob
SCI 340 L27 Simple Pendulum
Simple Pendulum q L m
Massless, inextensible string/rod
Point-mass bob 4

5. Question
The period of a simple pendulum depends on: A. The length L. B. The mass m. C. The maximum amplitude A. D. The gravitational field g.

6. Simple Pendulum Force SFT = –wT = –mg sinq L T = wR + mv2/L q
SCI 340 L27 Simple Pendulum
Simple Pendulum Force q L m
T = wR + mv2/L
w = mg q
wT = mg sinq
wR = mg cosq
SFT = –wT = –mg sinq

7. Simple Pendulum Torque
SCI 340 L27 Simple Pendulum
Simple Pendulum Torque q L m
SFT = –wT = –mg sinq
= LFT = –L mg sinq
Restoring torque 7

8. Small-Angle Approximation
SCI 340 L27 Simple Pendulum
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 Lmg
SCI 340 L27 Simple Pendulum
Simple Pendulum q L m
t = –L mg sinq
t  –L mg q = –kq
k = Lmg
I = mL2
Lmg
mL2
w2 = k/I =
= g/L
w is independent of mass m
(w is not the angular speed of the pendulum) 9

10. Board Work About how long is the pendulum of a grandfather clock?
SCI 340 L27 Simple Pendulum
Board Work
Find the length of a simple pendulum whose period is 2 s.
About how long is the pendulum of a grandfather clock?