Role of force in oscillatory motion?

[Elena14]

My textbook says, "Very often the body undergoing periodic motion has an equilibrium position somewhere inside its path."
" If a body is given a small displacement from the equilibrium position, a force comes into play which tries to bring the body back to the equilibrium point giving rise to oscillations and vibrations."

I have the following doubts-
a) What do they mean by "very often"? I can only think of circular motion as the only case where the equilibrium position is not inside its path? Am I correct? And what are some other examples of periodic motion which are not oscillatory motion?
b) When we are giving the body a small displacement, aren't we applying a force, and wouldn't this force be responsible for giving rise to oscillations and vibrations. Why did they say that the force comes into play after the particle has been displaced?
In the example of a motion of bob of a pendulum, what forces cause the bob to move for so long?

I am new to this topic, so please explain as simply as possible.

 

[mfb]

(a) circular, elliptical, or more complex patterns in at least two dimensions.
(b) It does not matter where the displacement comes from, as long as it is an external influence. You can put a new object in that position, for example. Afterwards you do not influence the system any more, and the internal forces in the system lead to an oscillation.

In the example of a motion of bob of a pendulum, what forces cause the bob to move for so long?

Gravity, a spring, or whatever is used in the pendulum.

 

[Elena14]

1)After the small displacement, a force comes into action which is responsible for oscillations.
2) The force that we apply to displace the bob of the pendulum will cause it to oscillate.
How can both these statements be same?

Will you please explain what do you mean by keeping a new object in that position?

 

[mfb]

2) The force that we apply to displace the bob of the pendulum will cause it to oscillate.

Ignore the details how we displace the pendulum. It just leads to confusion. Assume the pendulum is displaced at the start of the setup.

Will you please explain what do you mean by keeping a new object in that position?

Not keeping it there. We place it there, then we let it free.

 

[2nafish117]

(b) It is incorrect to think that the external force that you apply to displace the bob causes the periodic oscillations.Imagine that there is no restorative force on the system.(in a pendulum case it would mean there is no gravity) Now when you slightly push the bob(ie external force applied)
the system just moves forward and never comes back(ie bob just goes forward linearly with const velocity after your hands have lost contact with the bob).

But when there is a restorative force acting on the system(ie gravity) then the restorative force pushes the bob back to the mean position,where the net force on the system is zero(tension cancels the pull of gravity).here at the mean position the system(bob) has some momentum that causes it to cross the mean position and then the restorative force tries to pull it back in towards the mean position.

Your force only causes a displacement of the bob from the mean position so that the restorative force can start operating .The actual oscillation is due to the restorative force.