lecture_30 - MIT OpenCourseWare http://ocw.mit.edu 2.004...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 2.004 Dynamics and Control II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . A- A T = t A s i n ( B ) A s i n ( M t + B ) 2 F M Massachusetts Institute of Technology Department of Mechanical Engineering 2.004 Dynamics and Control II Spring Term 2008 Lecture 30 1 Reading: Nise: 10.1 1 Sinusoidal Frequency Response 1.1 Definitions Consider a sinusoidal waveform f ( t ) = A sin( t + ) where A is the amplitude (in appropriate units) is the angular frequency (rad/s) is the phase (rad) In addition we can define T the period T = 2 / (s) f the frequency, ( f = 1 /T = / 2 ) (Hz) 1 copyright c D.Rowell 2008 301 F ( t ) t I n p u t t o m a s s m F ( t ) f r i c t i o n B R e s p o n s e s t e a d y - s t a t e r e s p o n s e t r a n s i e n t r e s p o n s e v ( t ) m v ( t ) m The Euler Formulas: We will frequently need the Euler formulas e jt = cos ( t ) + j sin( t ) e jt = cos ( t ) j sin( t ) or conversely cos( t ) = 1 e jt + e jt 2 sin( t ) = 1 e jt e jt 2 j 1.2 The Steady-State Sinusoidal Response Assume a system, such as shown above, is excited by a sinusoidal input. The total response will have two components a) a transient component, and a steady-state component y ( t ) = y h ( t ) + y p ( t ) . We define the steady-state component as the particular solution y p ( t ). Let the system dif- ferential equation be d n y d n 1 y dy d m u d m 1 u...
View Full Document

Page1 / 8

lecture_30 - MIT OpenCourseWare http://ocw.mit.edu 2.004...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online