ch17 Flashcards
period T
The time taken for one complete oscillation or vibration
frequency f
number of oscillations per unit time
simple harmonic motion
motion of a particle about a fixed point such that its acceleration proportional to distance from the fixed point / displacement and is in the opposite direction
harmonic oscillator
A system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x and therefore follows simple harmonic motion
acceleration of simple harmonic motion equation
a=-w^2x
angular frequency
ω = 2πf /// 2π/T
displacement solution
x = x0 sinωt
velocity v of the particle when x = x0 sinω t eq
v = v0 cosω t
The maximum speed v0 eq
v0 = x0ω //// v0 = ±ω (x0^2-x^2)^1/2
acceleration a of
the particle when x = x0 sinω t
a = −a0 sinω t
kinetic energy at displacement x
Ek = 1/2mω 2(x0^2 −x^2)
restoring force
F res = −mω^2x
potential energy Ep at displacement x
Ep = 1/2mω ^2x^2
total energy Etot
Etot = 1/2mω^ 2x0^2
damped oscillations
reduction in amplitude / energy
due to force resistive forces
critical damping
Damping that causes the displacement to decrease to zero in the shortest time possible, without any
oscillation.
heavy damping
Damping that causes an exponential reduction in the amplitude of vibration of an oscillation, but over a greater time than for critical damping
oscillations
backward and forward motion (between two limits)
free oscillations
no external force acting on particle
forced frequency
frequency at which object is made to vibrate
natural frequency of vibration
frequency at which object vibrates when free to do so
resonance
maximum amplitude of vibration of oscillating body when forced frequency equals natural frequency
