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Reading: Chapter 4.

Exercises: 4.14, 4.17, 4.19 and 4.29.

For 4.14, also indicate how the solution would change if

• the rotational speed of the rollers is increased
• the coefficient of friction is increased
• the density of the board is increased and
• the length of the board is increased.

For problem 4.19 part 4, should we assume the initial value of b, or a decreased value?

garrett_schwartz wrote:For problem 4.19 part 4, should we assume the initial value of b, or a decreased value?

Use the initial value of b.

For 4.19:
to solve for wn I did sqrt(k) and got 94.87
-> for zeta I did b/2*wn... this leaves me with z=12.65
I'm not sure how to correlate this z to the Fig 4.20 because the highest z value is 1. I may have just completely solved for z incorrectly

kgilhoo1 wrote:For 4.19:
to solve for wn I did sqrt(k) and got 94.87
-> for zeta I did b/2*wn... this leaves me with z=12.65
I'm not sure how to correlate this z to the Fig 4.20 because the highest z value is 1. I may have just completely solved for z incorrectly

The natural frequency is sqrt(k/m) so should be 3. With that your zeta should be in the right range.

Thank you!

For question 4.29, is the equation x'' + 1/(5x') +... or x'' + (1/5)x' +...?

ccunnin6 wrote:For question 4.29, is the equation x'' + 1/(5x') +... or x'' + (1/5)x' +...?

The latter. The former would be nonlinear and also would not make any sense for vibrations.