Transcript Slide 1

SHM Kinematics
xt   xm cos t   
Where
xt   the position of the simple harmonic oscillator
as a function of time
xm  Amplitude
  angular frequency
t  time
  phase constant
SHM Kinematics
What about the velocity of a simple harmonic oscillator?
dx
vt  
dt
d
vt   xm cost   
dt
vt   xm sin t   
Velocity Amplitude
vm  xm
x and v in SHM
SHM Kinematics
What about the acceleration of a simple harmonic oscillator?
dv
at  
dt
d
at    xm sin t   
dt
at    2 xm cost   
Acceleration Amplitude
Remember
am   2 xm
xt   xm cost   
at    2 xt 
x, v and a in SHM
SHM Kinematics
What about the Force that results in simple harmonic motion?
at    2 xt 
F  ma


F   m 2 x
Simple Harmonic Motion is the motion executed by a particle of mass m subject to a
force that is proportional to the displacement of the particle but opposite in sign.