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 𝐴 oscillating through an angle of 2πœƒ, where tanπœƒ=43. Find the speed of the ball at the point 𝐡, given that it is the midpoint of the ball’s path. Take the acceleration due to gravity 𝑔=9.8/ms.

  • A42√110 cm/s
  • B14√330 cm/s
  • C70√66 cm/s
  • D28√165 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 𝐡, 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 π‘™οŠ§ has a period of π‘‡οŠ§. If the pendulum’s length is decreased by 19%, the period becomes π‘‡οŠ¨. Find the ratio of π‘‡π‘‡οŠ¨οŠ§ to three decimal places.

Q4:

The simple pendulum shown starts moving from rest at position 𝐴 with angle πœƒ=20∘. Given that the pendulum’s length is 39.2 m, find an equation for the angle in degrees in terms of time 𝑑. Take the acceleration due to gravity to be 9.8 m/s2.

  • Aπœƒ(𝑑)=20ο€Ό12𝑑+πœ‹οˆsin
  • Bπœƒ(𝑑)=20(2π‘‘βˆ’πœ‹)cos
  • Cπœƒ(𝑑)=20(2𝑑)cos
  • Dπœƒ(𝑑)=20ο€Ό12π‘‘οˆsin
  • Eπœƒ(𝑑)=20ο€Ό12π‘‘οˆcos

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