Forced Oscillations Damped 12/9/2018 Forced Vibration- Damped Case

F(t) : general time dependent External Force is F(t) : general time dependent 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Forced oscillator:Damped case Time dependent function 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Companion equation: 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Complementary function: Transients Try steady state solution (Particular solution) Find 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Complementary function: Transients Try steady state solution (Particular solution) Find 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Amplitude: 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Phase: 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Show amplitude resonance at: 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Forced oscillations for different resistances 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Amplitude and phase 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Different driving amplitudes 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Instantaneous power absorbed by the system: Average power over one cycle: 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Peak Power: Width at half peak power = 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Averaged power absorbed = < P > / 2 = 3 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Stored energy: Problem: What is the peak value and for what driving frequency? 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Stored energy: < E > = 3 12/9/2018 Forced Vibration- Damped Case

Forced Vibration- Damped Case Resonant quality factor: 12/9/2018 Forced Vibration- Damped Case

F(t) : Sin(wt) or Cos(wt) External Force is F(t) : Sin(wt) or Cos(wt) 12/9/2018 Forced Vibration- Damped Case

Forced Oscillations Solution=Complementary Function + Particular Integral

Solutions Complementary Functions are transients Steady State behaviour is decided by the Particular Integral

Solution with Damping

Amplitude and Phase (again)

Amplitude and Phase (again) -

Some Key Points High frequency and low frequency behaviour unchanged by damping Amplitude is finite throughout Maximum Amplitude at

Average Energy PHYSICS 1

Average Energy Plot

Mild Damping Maxima at

Mild Damping Maxima at

FWHM FHWM=

Power

Average Power Using

Average POwer

Lorentzian Profile