Download Simple Harmonic Motion

Simple Harmonic Motion
 Simple Harmonic Motion – Vibration about
an equilibrium position in which a
restoring force is proportional to the
displacement from equilibrium.
 A mass-spring system is an example of
simple harmonic motion.
 Hooke’s Law
Spring force = -(spring constant x
displacement)
Felastic = -kx
Hooke’s Law cont.
 At the equilibrium position, velocity is at maximum,
spring force and acceleration are zero.
 At maximum displacement, spring force and
acceleration is a maximum and velocity is at zero.
 The negative sign in the equation signifies that the
direction of the spring force is always opposite the
direction of the mass’s displacement.
 The term k stands for spring constant.
 A greater value for k means a stiffer spring because a
greater force is needed to stretch or compress it.
 The SI units of k are N/m.
Measuring Simple Harmonic Motion
 For small angles, a pendulum’s motion is
simple harmonic.
 Amplitude – The maximum displacement
from equilibrium.
 Period – The time it takes to execute a
complete cycle of motion.
 Frequency – The number of cycles or
vibrations per unit of time.
 Period and frequency measure time.
 Frequency is the reciprocal of the period.
Cont.
 Equations:
f = 1/T
 The SI unit of frequency is Hertz (Hz)
or 1/s.
T = 1/f
 The SI unit of period is the second
(s).
Period of a Simple Pendulum
 The period of a simple pendulum depends
on string length and gravity.
 Equation:
T = 2√L/g
Period = 2 x square root of (length divided
by free-fall acceleration)
Period of a Mass-Spring System
 The period of a mass-spring system
depends on mass and the spring constant.
 Equation:
T = 2√m/k
Period = 2 x square root of (mass divided
by spring constant)
Homework
 Pg. 441 2-3
 Pg. 445 1 and 3
 Pg. 449 1 and 2
 Pg. 451 1 and 2 top of page
 Pg. 451 1 and 2 bottom of page