A simple pendulum of length 1 m with small amplitude has period approximately?

• A. 1.22 s
• B. 2.01 s
• C. 1.00 s
• D. 3.14 s

Answer: (B)

A pendulum with a small swing behaves like a simple harmonic oscillator, so its period is determined by T = 2π sqrt(L/g). With a length of 1 meter and g about 9.8 m/s^2, the period becomes T ≈ 2π sqrt(1/9.8) ≈ 2π × 0.319 ≈ 2.01 seconds. So the swing takes a little over two seconds for each full cycle. The other times would require different lengths (for example, a much shorter length gives about 1 second, while a much longer length gives around 3 seconds), which doesn’t match a 1 m length.