Oscillatory Motion EXAMPLES

1
Chapter 15

• Oscillatory Motion EXAMPLES

2
Chapter 15 Oscillatory Motion EXAMPLES
3
Example 15-1 Motion of the Block (Horizontal)

• The block continues to oscillate between
  A and A
• These are turning points of the motion
• The force F is conservative
• In the absence of friction, the motion will
  continue forever
• Real systems are generally subject to friction,
  so they do not actually oscillate forever

4
Example 15-1 Motion of the Block (Vertical)

• When the block is hung from a vertical spring,
  its weight will cause the spring to stretch
• Figure (a) Free spring, hang vertically
• Figure (b) Mass m attached to spring in new
  equilibrium position, which occurs when
• ?F mg kxo ? xo mg/k
• If the resting position of the spring is defined
  as x 0, the same analysis as was done with the
  horizontal spring will apply to the vertical
  spring-mass system

5
Example 15-2 Conceptual Example(SHM Forces)

• Which of the following represent an object
  undergoing
  
• SHM
• (a). F 0.5x2
• (b). F 2.3y
• (c). F 8.6x
• (d). F 4?
• Answer
• (b). F 2.3y (d). F 4?
• Force has minus sign required to restore the
  system to equilibrium.
• Force is proportional to a displacement
• (which need not to be x).

6
15-3 SHM Example 1

• Initial conditions at t 0
• x (0) A
• v (0) 0
• This means f 0
• The velocity reaches extremes of ?A
• The acceleration reaches extremes of ?2A

7
15-3 SHM Example 2

• Initial conditions at t 0
• x (0)0
• v (0) vi
• This means f - p/2
• The graph is shifted one-quarter cycle to the
  right compared to the graph of x (0) A

8
Example 15-4 Conceptual Example (Doubling
Amplitude)

• Suppose the spring from figure is stretched twice
  as far (to x 2A). What happened to
  E, vmax, amax?
• (a). E ½kA2 (15.21)
• (b). vmax ?A (k/m)½A (15.17)
• (c). amax ?2A (k/m)A (15.18)
• Answers
• (a). E ½k(2A)2 4( kA2)
• So stretching A twice as far, quadruples the
  energy
• (b). vmax ?(2A) 2?A
• So stretching A twice as far, doubles the
  maximum velocity
• (c). amax ?2(2A) 2?2A
• So stretching A twice as far, doubles the
  maximum acceleration

9
Material for the Midterm

• Material from the book to Study!!!
• Objective Questions 12-14
• Conceptual Questions 3-5
• Problems 5-8-14-18-21-25