12B x,v,a eqns for SHM

12B x,v,a eqns for SHM - 3/31/2011 SHM: Mathematical Model...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
3/31/2011 1 Physics 1C Lecture 12B "Imagine if we taught baseball the way we teach science. Undergraduates might be allowed to reproduce famous historic baseball plays. But only in graduate school would they, at last, actually get to play a game." --Alison Gopnik SHM: Mathematical Model Equations of motion for SHM: Remember, simple harmonic motion is not uniformly accelerated motion SHM: Mathematical Model The maximum values of velocity and acceleration for an object in SHM: The velocity is 90 o out of phase with the displacement and the acceleration is 180 o out of phase with the displacement SHM – Example 1 Initial conditions at t = 0 are: x (0)= A and v (0) = 0 This means f = 0 The acceleration reaches extremes of w 2 A The velocity reaches extremes of A SHM – Example 2 Initial conditions at t = 0 are: x (0)= 0 and v (0) = V i This means = - p /2 The graph is shifted one- quarter cycle to the right compared to the graph of x (0) = A Mass-Spring Energy Let’s assume a spring-mass system is moving on a frictionless surface This is an isolated system, therefore the total energy of the system is constant The kinetic energy is: KE = 1/2 mv 2 = 1/2 m 2 A 2 sin 2 ( t + ) The elastic potential energy is: PE = 1/2 kx 2 = 1/2 kA 2 cos 2 ( t + ) The total energy is: KE + PE = 1/2 kA 2
Background image of page 1

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

View Full DocumentRight Arrow Icon
3/31/2011 2 Mass-Spring Energy Let’s assume a block moves to the right ( +x ) at an initial velocity, v i , on a frictionless surface toward an unstretched spring with spring constant, k : Initially, the total mechanical energy of the system
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/11/2012 for the course PHYS 1C 1C taught by Professor Wethien during the Spring '11 term at UCSD.

Page1 / 4

12B x,v,a eqns for SHM - 3/31/2011 SHM: Mathematical Model...

This preview shows document pages 1 - 3. Sign up to view the full document.

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