Why is a simple pendulum not a perfect simple harmonic oscillator?

[Huzaifa]

Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?

 

[jbriggs444]

Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?

Is the restoring torque exactly proportional to the angle of the pendulum? What happens if the angle gets big?

 

[hutchphd]

Because the restoring force is not exactly (negatively) proportional to the displacement.

 

[Baluncore]

Here are some better approximations for the period.
http://www.leapsecond.com/hsn2006/pendulum-period-agm.pdf
http://www.leapsecond.com/hsn2006/

 

[kuruman]

Yes, the simple pendulum is not a simple harmonic oscillator for reasons already explained. However, Christiaan Huygens's pendulum follows the tautochrone curve which is not as simple as a circle but has amplitude-independent period, i.e. is a simple harmonic oscillator.