DEPARTMENT
MEC702_Wk_7_Tutorial

# MEC702_Wk_7_Tutorial - MEC702 Wk 7 Tutorial Modeling 1 If a...

• Homework Help
• 1

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: MEC702 Wk 7 Tutorial Modeling 1. If a massspring system with an iron ball of weight 98 nt (about 22 lb) can be regarded as undamped, and the spring is such that the ball stretches it 1.09 m (about 43 in.), how many cycles per minute will the system execute? What will its motion be if we pull the ball down from rest by 16 cm (about 6 in.) and let it start with zero initial velocity? (Solution: y(t) = 0.16 cos 3t) 2. How does the the motion in Question 1 above change if we change the damping constant c from one to another of the following three values, with y(0) = 0.16 and y 0 (0) = 0 as before? (a) Case I: c = 100 kg/sec (b) Case II: c = 60 kg/sec (c) Case III: c = 10 kg/sec 3. If a weight of 20 nt (about 4.5 lb) stretches a certain spring by 2 cm, what will the frequency of the corresponding harmonic oscillation be? The period? 4. Show that in the overdamped case, the body can pass through y = 0 at most once. 5. Show that the maxima of an underdamped motion occur at equidistant t-values and nd the distance. Higher Order Linear Homoegeneous ODEs 1. Solve the given ODEs. (a) y 000 + 25y 0 = 0. (b) y iv + 2y 00 + y = 0. (c) y iv − 4y 00 = 0. (d) (D3 − D2 − D + 1)y = 0. 2. Solve the given IVP. (a) y iv − 9y 00 − 400y = 0, y(0) = 0, y 0 (0) = 0, y 00 (0) = 41, y 000 (0) = 0. (b) 4y 000 + 8y 00 + 41y 0 + 37y = 0, y(0) = 9, y 0 (0) = −6.5, y 00 (0) = −39.75. 1 ...
View Full Document

• Winter '16
• Alveen Chand
• 2 cm, 4.5 lb, 1.09 m, corresponding harmonic oscillation, Linear Homoegeneous ODEs

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern