A pendulum of length 1.5 m swings through a small angle $\theta\,$ radians from the vertical.

The horizontal displacement of the pendulum bob from the vertical is $x\,$ metres, where $1.5\sin\theta$ .

The vertical rise of the bob above its lowest point is $h\,$ metres, where $\cos\theta)$ .

Use small angle approximations to show that, for small $θ\theta$ ,

$h≈x23\displaystyle h \approx \frac{x^2}{3}$

Use this result to estimate the vertical rise of the bob when its horizontal displacement is 0.12 m.

State one reason why this approximation would be unreliable for a horizontal displacement of 1.2 m.

A pendulum of length 1.5 m swings through a small angle $\theta\,$ radians from the vertical.

The horizontal displacement of the pendulum bob from the vertical is $x\,$ metres, where $1.5\sin\theta$ .

The vertical rise of the bob above its lowest point is $h\,$ metres, where $\cos\theta)$ .

Use small angle approximations to show that, for small $θ\theta$ ,

$h≈x23\displaystyle h \approx \frac{x^2}{3}$

Use this result to estimate the vertical rise of the bob when its horizontal displacement is 0.12 m.

State one reason why this approximation would be unreliable for a horizontal displacement of 1.2 m.

1.8 E: Trigonometry

1.8 E: Trigonometry Questions