Question about force in transverse waves on a string

In deriving wave equation or power transmission of wave transmitted by a string, it is usually stated (with some assumptions) that the transverse force on a point of the string is proportional to the slope at that point. An example is given in p.20 of this notes.

If the slope is zero the transverse force is also zero. It can also be seen in the way that if some portion of the string is horizontal the tensions on both side are also horizontal and thus cancel out, therefore no transverse force.

However, in the case that the wave is sinusoidal, the points at the amplitude of the wave should have greatest acceleration and should experience the greatest force because every point is performing SHM. There seems like a contradiction here. Why?

• "points at the amplitude of the wave"... what does that mean? – DanielSank Jul 1 '15 at 20:30
• @DanielSank It is the portion of string at the maximum position of the string in a sinusoidal wave. – Kelvin S Jul 2 '15 at 10:33