# 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 ballβs 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/s^{2}.

**Q3: **

A pendulum of length has a period of . If the pendulumβs 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 pendulumβs 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/s^{2}.

- 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/s^{2}.

**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/s^{2}.

**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/s^{2}.

**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/s^{2}
and on the Moon to be 1.6 m/s^{2}.