Question

The pendulum on a grandfather clock swings from side to side once every second. If the length of the pendulum
is 7 feet and the angle through which it swings is 20°, how far does the tip of the pendulum travel in 1 second?

Answer 1

Answer:

Since the pendulum moves from side to side in 1 sec, the length of the arc covered by the pendulum in an oscillation will be the length travelled in 1 sec

From trigonometry, we know the relation:

Θ(in radians) = l / r (where r is the length of the pendulum and l is the length of arc travelled)

But first, we need to convert 20 degrees to radians

20 degrees = π/9 radians

r = 7 feet

Now, plugging these values in the equation:

π / 9 = l / 7

l = 7π / 9 feet

l = 2.44 feet (approx)