Intermediate Mechanical & Space Dynamics - Quiz PDF

Preview

Summary

Intermediate Mechanical & Space Dynamics - Quiz...

Description

MECH2210, Part A Quiz Student Number

Given Name

First Name

Notes:  Ensure that you have filled in your details above  Only answers in this answer booklet will be marked.  Only the results entered in the boxes provided will be marked.  If we suspect that you are not going to submit the results of your own work, we will take your answer booklet and you will receive a mark of 0 for this assessment item of the course.

Question 1 Derive the equation of motion for the system below, which is shown in its equilibrium position. Neglect the mass of link AOB and assume small oscillations.

x

x

Determine the characteristic vibration parameters. Give n as a function of m1, m2, c, k, a and b. You can refer to previously calculated quantities for  and d.

n 



d 

Question 2 A commercial m = 35 kg washing machine, including wet clothing, has a drum radius r = 0.3 m and sits on four identical spring mounts, which have a static displacement of 10 mm.

m x

r  me

What is the amplitude of vibration X in millimetres, if a wet me = 500 g clump of clothes is stuck to the drum as shown when the washing machine is in the spin cycle, rotating at  = 275 rpm?

X Is there any danger that the machine is going to pass through its resonance frequency when it spins up to or slows down from the spin cycle?

Note: The magnification relation for excitation by a rotating unbalance is:

X  m e  e   m   

   n

2

M

with

1

M  1  

   n

2

2

   2  

   n

2

Question 3 The block m is suspended from two pulleys, which each have stiffness k. Neglect the mass of the pulleys.

m x

Use energy method to determine the equation of motion and natural frequency of the vertical oscillations of the system, if x is measured from the static equilibrium position.

Total kinetic energy:

T

Total potential energy:

V

Equation of motion:

Resonant frequency:

x

n 

Question 4 A mass m1 = 2 kg impacts a horizontal beam AOB (mass m2 = 8 kg, length L = 2 m) with velocity v = 12 m/s. The impact is totally unelastic, i.e. mass and beam move together after the impact.

m1  v



O

A L/4

L/4

m2

B

L/2

What is the angular momentum in analytical form before impact?

H 01  What is the angular momentum in analytical form after impact?

H 02  What is the angular velocity  in rad/s after impact?

 What is the maximum angle  in degrees that is reached after impact, if friction in the pin support O is ignored?

max ...