Chapter 10 Oscillations Flashcards
(13 cards)
Conditions for simple harmonic motion
Acceleration is directly proportional to the displacement from equilibrium
Acceleration is always directed towards equilibrium position
a = -ω^2 x
ω = 2πf
Variation of x with time t
x = X0sin(ωt)
Velocity formula for simple harmonic motion
v = +-√((X0)^2-x^2)
Total energy in terms of potential and kinetic energy
Umax
Kmax when Umin can be assumed to be 0
Maximum KE
1/2 m v0^2
1/2 m ω^2 X0^2
Free oscillation
There is neither resistive forces nor driving forces acting on the system. Thus total energy is always constant and it oscillates with constant amplitude
In a free oscillation the object oscillates with frequency called its natural frequency
Damped oscillation
One that experiences resistive forces
Oscillating system loses energy until it comes to a stop
Under damping
Amplitude gradually decrease with time but period remains constant over time
Period is higher than undamped system
Greater the degree of damping, the more drastic the decrease in amplitude
Critical damping
Body does not oscillate but returns to equilibrium position in the shortest possible time
Overdamping
Body takes a long time to return to its equilibrium position without oscillating
Forced oscillation
Driven by external periodic driving oscillator or driver. Continuous energy input to the oscillating system by the driver and system oscillates at frequency of the driver
Resonance
When the oscillating system achieves maximum amplitude. In an undamn system resonance occurs when the driving frequency equals the natural frequency of the oscillating system
Features of resonance curve
Curve shifts lower with increased damping
Flatter peak at resonance with increased damping
Peak skewed to the left with increased damping
