P H Y S I C S   

Chapter 7: Waves and Vibrations

Section 7B: SHM of a Pendulum

Bell Ringer

What is the period of a spring-mass system in which a 3.5kg mass is displaced 1.5m on a spring with a constant of 2.5N/m?

Period of Pendulum

(1564-1642)

Galileo Galilei

xo = 0 equilibrium

Simple Harmonic Motion (SHM) Pendulum approximates SHM when

oscillated with an initial angle of 15o or less

T period (s) l length (m) g acceleration due to gravity (m/s2)

Period of a Pendulum

Depends on: Length gravity

Period of a Pendulum Demo

Does NOT depends on: mass amplitude

Maximum velocity occurs at equilibrium Zero velocity at amplitude

Velocity

maxvelocity

zerovelocity

zerovelocity

Frequency Equation

f frequency (Hz) T period (s)

In-Class Problem #1

A pendulum of mass 1.5 kg has a length of 0.15 m. Determine (a) the period and (b) frequency of the pendulum.

T = 0.78 s

f = 1.29 Hz

In-Class Problem #2

If a pendulum has a period of 2.0 s on Earth determine its period on the Planet Hoth where the acceleration due to gravity is 13.2 m/s2.

l = 0.99 m

T = 1.72 s

Assignment

Problem Set 7B 7A-7B Quiz (Simple Harmonic Motion)