MECH226 Vibrations Tutorials



MECH226     Vibration Tutorial 1
MECH226     Vibration Tutorial 2


Welcome to these web pages.  There are two tutorial sheets, each with 5 questions.  Tutorial Sheet 1 is on Free Vibration, while Tutorial Sheet 2 is on Forced Vibration.

Some guiding principles

(1)  Try and establish how the system may be modelled, by asking yourself the following questions:

(a) Is the vibration free or forced?

If free, then it might be given a small displacement or an initial velocity and then left to oscillate.

If forced, then the vibration will be sustained, either by an applied force or by the motion of the support.

(b)  Is there any damping?

If the answer is NO, then thel damping terms c = z = d = 0;  the amplitude of free vibration will not change with time.

If the answer is YES, however, then you will need to establish a value for either c or z; the amplitude of free vibration will get smaller with time.

(2)  Once you have established the model, look up the relevant equations.

(3)  Start each problem by writing down all the information you are given, using the appropriate symbols.  You will need sometimes to distinguish between damping constant, c, and damping ratio, z, so read the problem carefully.  

(4) Then write down what you are being asked to find.

(5) Collect together all the relevant equations.   Usually, you will need to undertake some  manipulation of the equations to obtain the desired result.


Each tutorial sheet consists of five questions and is on a separate page.

The answer to each question is given on the tutorial sheet.  In addition, for each question a hint is  provided in case  you are not sure where to start, from which you can go to the solution.  You can also go to the solution directly from each question on the tutorial sheet.

Although solutions are also provided, it is strongly recommended that you try working through each question yourself, and only look at  the solution when you have come up with an answer, or are completely stuck, even after reading the hint.

The equations referred to in the solutions are those in the notes accompanying this section of the module. 

If you have any questions, please send me an e-mail:

Miggy Singh

April 2003