# Worksheet: The Simple Pendulum

This worksheet evaluates your understanding about how to model the simple pendulum motion using simple harmonic motion and the factors affecting the period of the simple pendulum.

Q1:

The figure shows a simple pendulum consisting of a ball attached to the end of a light inextensible string of length 165 cm. The pendulum started moving from rest from point oscillating through an angle of , where . Find the speed of the ball at the point , given that it is the midpoint of the ball’s path. Take the acceleration due to gravity . • A cm/s
• B cm/s
• C cm/s
• D cm/s

Q2:

A light inextensible string of length 32 cm is used to hang a pendulum. If the pendulum starts moving from rest from point , how many times will the pendulum pass by the equilibrium position after 2 seconds? Take the acceleration due to gravity to be 9.8 m/s2. Q3:

A pendulum of length has a period of . If the pendulum’s length is decreased by , the period becomes . Find the ratio of to three decimal places.

Q4:

The simple pendulum shown starts moving from rest at position with angle . Given that the pendulum’s length is 39.2 m, find an equation for the angle in degrees in terms of time . Take the acceleration due to gravity to be 9.8 m/s2. • A
• B
• C
• D
• E

Q5:

The given pendulum started moving from rest from point . Given that it has a length of 49 cm, find the time in seconds it takes to move from point to point . Give your answer to the nearest three decimal places. Take the acceleration due to gravity to be 9.8 m/s2. Q6:

What is the frequency of a pendulum that has a length of 0.3 m? Give your answer to the nearest two decimal places. Take the acceleration due to gravity to be 9.8 m/s2.

Q7:

What is the length of a pendulum that has a period of 1 s? Give your answer to the nearest two decimal places. Take the acceleration due to gravity to be 9.8 m/s2.

Q8:

Which of the following pendulums has a higher frequency: pendulum A of mass 2 kg and length 1 m or pendulum B of mass 10 kg and length 1.5 m?

• APendulum B
• BPendulum A

Q9:

If a pendulum of length m has a period of on Earth and a period of on the Moon, find the ratio of to the nearest two decimal places. Consider the acceleration due to gravity on Earth to be 9.8 m/s2 and on the Moon to be 1.6 m/s2.