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In this lesson, we will learn how to apply the equations of simple harmonic motion to oscillating pendulums, referring to the lengths of such pendulums.

Q1:

Find the ratio of the periods of a pendulum if the pendulum is first used on Earth and then on the Moon. Use a value of 1.63 m/s^{2} for the acceleration due to gravity on the Moon.

Q2:

What is the length of a pendulum that has a period of 0.941 s?

Q3:

A steel ball with a mass of 125 g is attached to a 1.50-m-length string of negligible mass. The string is hung from a horizontal platform to form a pendulum. The ball is displaced so that the string is taut and aligned at a 3 5 . 0 ∘ angle from the vertical. The ball is then released.

What is the speed of the steel ball when the string points vertically downward?

What is the speed of the steel ball when the string is aligned at a 1 5 . 0 ∘ angle from the vertical?

What is the speed of the steel ball when the string is aligned at a 2 5 . 0 ∘ angle from the vertical?

Q4:

A pendulum has a period of 2.00000 s in a location where the acceleration due to gravity is 9.80000 m/s^{2}. The pendulum is moved to a new location where its period is 1.99796 s. What is the acceleration due to gravity at its new location?

Q5:

Two parakeets sit on a swing with their combined centre of mass 10.0 cm below the pivot. At what frequency do they swing?

Q6:

A pendulum that has a period of 3.00000 s is located at a point where the acceleration due to gravity is 9.79000 m/s^{2}. The pendulum is moved to a location where the acceleration due to gravity is 9.82000 m/s^{2}. What is its new period?

Q7:

Suppose the length of a clock’s pendulum is increased by 1 . 6 0 0 % at exactly noon one day. What time will the clock read 24.00 hours later assuming that the pendulum has kept perfect time before the change?

Q8:

If a pendulum-driven clock gains 5.00 s/day, what fractional change in pendulum length must be made for it to keep perfect time?

Q9:

A pendulum of length 𝑙 1 has a period 𝑇 1 . 𝑙 1 is decreased by 9 . 0 0 % . The pendulum’s new period is 𝑇 2 . What percent of 𝑇 1 is 𝑇 2 ?

Q10:

A pendulum of length 𝑙 1 has a period 𝑇 1 . A different pendulum has a length 𝑙 = 3 . 0 0 𝑙 2 1 and a period 𝑇 2 . Find 𝑇 𝑇 2 1 .

Q11:

A child on a swing moves from a point of maximum displacement from equilibrium and then returns to that point. How long does the motion take if the child’s centre of gravity is 4.00 m below the pivot of the swing?

Q12:

What is the frequency of a 2.5-meter-long pendulum?

Q13:

The pendulum on a cuckoo clock is 7.25 cm long. What is its period?

Q14:

A pendulum clock made to be used on Earth is taken to Mars. Determine the time taken for the clock’s hour hand to complete a revolution of the clock’s face. Use a value of 3.71 m/s^{2} for the acceleration due to gravity on Mars.

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