Why must the angle through which the pendulum swings be not more than 5 degrees?

Answer 1

The period of simple pendulum is given by the formula
T = 2π √ [L/g].

This formula is derived assuming that the angle must be small.

How small? It is so small that sin θ is nearly equal to θ

When θ = 5° = 0.0873 radian, sin θ = 0.0871
When θ = 10° = 0.1745radian, sin θ = 0.1736
When θ = 15° = 0.2618 radian, sin θ = 0.2588

It is seen from above the period will not change very much even if the angle is 10°
The result depends upon how much sin θ differs from θ

Answer 2

I'm not sure where this restriction of 5 degrees came from. I suspect your teacher was telling you that the solution to the equation of motion for a pendulum can be simplified and solved in closed form if the angle of displacement of the pendulum is small. Otherwise, the frequency and amplitude start to couple and the period of motion no longer obeys the simple relationship of sqrt(g/l).

Answer 3

A rigid pendulum can swing up to +/- 180 degrees, exclusive, but its period would depend strongly on angle. For small angles, though, the period is approximately constant, being describable as a harmonic oscillator. Anything up to +/- 5 degrees would have the same period to within a percent or two.

Answer 4

To solve the equation of motion for simple harmonic motion for any pendulum means making an approximation that


sintheta = theta in radians.

This is a good approximation for theta less than 5 degrees. For bigger angles you have to use consevation of energy, not the easier torque = I alpha equation. If that means nothing to you, just ignore it.

Answer 5

Because the elephant should not spook the mouse.