{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

16 frequency response

# 16 frequency response - 18.03 Lecture#16 Oct 14 2009 notes...

This preview shows pages 1–2. Sign up to view the full content.

18.03 Lecture #16 Oct. 14, 2009: notes The syllabus topic for today is frequency response . The idea is to understand the response of a system to sinusoidal input. There are two big points to be made. First is to understand what resonance means. Second is to extend our spring-and-dashpot example to cover electrical circuits. After those two things, I’ll say what I can about the mathematics of resonance. What’s resonance? The short answer is that many physical systems respond more strongly when they are driven at something like their natural frequencies. A simple physical example is a child’s swing. Left to itself, the swing will oscillate with a certain period. If it’s pushed periodically, it will begin to oscillate at the frequency with which it’s being pushed. If that frequency matches the swing’s natural frequency, then the amplitude of the oscillation will grow and grow. Here’s a mathematical version of this example. Start with the second order equation y ′′ + y = 0 . (Harmonic oscillator) This is the spring-and-dashpot system with mass m = 1, spring constant k = 1, and no damping. This equation appears all over the place in physics, because of examples like the spring and like the pendulum: it describes lots of physics exactly, and it’s a good approximation to lots more. You know that the general solution to the equation is y h ( t ) = A cos( t ) + B sin( t ) = C cos( t - φ ) . The subscript h stands for “homogeneous.” This means that the system oscillates with period 2 π in a purely sinusoidal fashion.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

16 frequency response - 18.03 Lecture#16 Oct 14 2009 notes...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online