SIMPLE HARMONIC MOTION

SIMPLE HARMONIC MOTION

1. restoring force is directly proportional to displacement from equi. point

   • F= -kx a= -w^2x 
   • REPRODUCTION

2. requirements

   • mass
   • linear restoring force

3. characteristic

   • periodic
   • same frequency
   • oscillation - same oscillation
   • linear restoring force

4. oscillation loaded spring

5. parameters

   • displcacement (x)
   • amplitude (A)
   • period (T)
   • frequency (f)
   • angular frequency (w)
   • phase angle (@)

6. kinematics

   • displcacement
     • x= A cos @= x[max] cos wt
       • A=x[max]
       • @=wt
     • at x-axis
     • @=wt, w is constant. t is independent (outside the circle)
     • Enter text here
   • velocity
     • -Aw sin wt
       • because the velocity is moving to the left, it have -(ve) sign
         • shm
       • we use sin bcoz the @ is on the P point, not Q
   • acceleration
     • do not fixed with time
     • a=-xw^2, x is displacement
     • have max acceleration at max -,+(x)
   • w (angular speed) = the number of radian it move through per second
     • 2(pai)f, f-is constant in 1 frequency for 1 cycle
     • 2(Pai)f=2pai/T

7. system

   • oscilaltion spring
   • pendulum

8. damping, forcing & resonance

   • damping
   • forced oscilation & resonance
   • self-excited vibration