Tension in a Pendulum: Exploring Horizontal Component and Restoring Force

[Carbon123]

1. The problem statement, all variables and given/knowns
So basically,I am confused by this quote in David Morin's Problems and Solutions in Introductory Mechanics that says:
the tension in the tilted string has a nonzero horizontal component (except at the highest points where the tension is zero and the lowest point where the string is vertical).

Morin, David. Problems and Solutions in Introductory Mechanics (p. 52). . Kindle Edition.
Doesn't T have a value that is M g cosx at the highest point ?

Homework Equations

∑F=m^ωr

The Attempt at a Solution

If there is no Tension then what is causing the acceleration to have a horizontal component ? (because Mg is Pointing downwards)Is it Mg sinx ?
Thanks in Advance

 

[haruspex]

except at the highest points where the tension is zero

That would be true if, and only if, the string is horizontal at the highest point. Is that the set-up being discussed?

Doesn't T have a value that is M g cosx at the highest point ?

Yes.

 

[Carbon123]

That would be true if, and only if, the string is horizontal at the highest point. Is that the set-up being discussed?

Yes.

That would be true if, and only if, the string is horizontal at the highest point. Is that the set-up being discussed?

Yes.

Thanks for replying.It says that the string was tilted.So,was the book incorrect ? What is the restoring force during a pendulum's oscillation ?

 

[haruspex]

Thanks for replying.It says that the string was tilted.So,was the book incorrect ? What is the restoring force during a pendulum's oscillation ?

The book is incorrect to say there is no horizontal component to the tension when the pendulum is at its highest point.
You asked, previously:

Doesn't T have a value that is M g cosx at the highest point ?

and I confirmed that, but that is the whole tension. What is the horizontal component of that?

Regarding restoring force, that's slightly ambiguous. You can consider the horizontal component of tension, or the tangential component of gravity. For small angles the difference is unimportant. In a thorough treatment, the tension at some point of the swing would also have a centripetal component. So I am not certain how to advise you without seeing the whole question.