5. FORCED VIBRATIONS
Free vibrations are those in which when a system is displaced
slightly from its mean position and then it vibrates with its own
force.
It is an ideal case. As mass spring system , simple pendulum
Forced vibrations are those vibrations in which a system
oscillates with the action of some external driving force or forces
that continue to act on after t = 0 . Force should be periodic in
nature.
6. EQUATION OF MOTION FOR FORCED VIBRATIONS
Forced vibrations are frequently seen in many mechanical systems .
In some cases these are called mechanical vibrations because there is mechanical
force behind it. Which is periodic
as example.
Running engine of car
Washing Machine
So equation of forced vibrations looks like
A
Where K → constant P → amplitude and w is frequency of force.
This is also known as general periodic function.
The above equation is a non-homogenous function.
7. SOLUTION:
The general solution for this equation can be found by solving
a particular solution.
This general solution corresponds to a particular solution of a
homogenous equation
We will guess a solution of this homogenous equation as:
→it’s a homogenous
deferential equation
1
8. by putting the respective derivatives of 1 in eq. A
If then blow up (destroy). Here is
magnification factor
9. GRAPHICAL EXPLANATION
If the system is in resonance then amplitude becomes infinite.
In real case amplitude does not goes infinite because there are
some damping forces.
10. PROBLEM NO. 1
1. A 1000 KG car carrying four 82 KG of each person travels over washboader
dirt road with corrugation 4.o m apart. The car bounces with maximum
amplitude when its speed is 16 km/h. when car stops and peoples get out
of car, how much does the car rise on its suspensions.
11.
12. PROBLEM# 2
.
Hanging from a horizontal beam are 5 pendulums of following
lengths a)0.10 m b) 0.30 c)0.40 d)0.80 e)1.2m suppose beam
goes under horizontal oscillations with angular frequencies in
range of 2.0 rad/s to 4.0 rad/s. which pendulum have large
amplitude?