1. Simple Pendulum
Question 1: If a pendulum takes 6 seconds to swing in each direction, find the length of the
pendulum.
Length = ____________m
Question 2: A pendulum with string length of 16cm is dropped from a small angular
displacement. Find the angular frequency and period.
Angular frequency = _____________rad/s
Period = ________________s
Question 3: A simple harmonic oscillator takes 15s to complete 5 vibrations. Find the period,
frequency, and angular frequency.
Period = _____________
Frequency = _____________
Angular frequency = _____________
2. Solutions
Question 1:
We know from the question that T=6s.
So 𝑇 = 2𝜋√
𝑙
𝑔
Solving for l, 𝑙 =
𝑔𝑇2
4𝜋2
=
9.8×62
4𝜋2
= 8.94𝑚
Question 2:
To find the angular frequency we use the formula 𝑤 = √
𝑔
𝑙
= √
9.8
16×10−2
= 7.83𝑟𝑎𝑑/𝑠
To find the period, we use the formula 𝑇 = 2𝜋√
𝑙
𝑔
= 2𝜋√
16×10−2
9.8
= 0.80𝑠
Question 3:
To find the period, simply do time taken divided by vibrations completed, as that will give the
time taken for one completely vibration. The period in this case is 15/5=3s.
To find the frequency, f = 1/T = 1/3 = 0.333Hz
To find the angular frequency, w= 2π/T = 2π/3 = 2.09rad/s
