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A simple pendulum and a mass–spring system each have a time period $T$ on the Earth - AQA - A-Level Physics - Question 30 - 2021 - Paper 1

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A simple pendulum and a mass–spring system each have a time period $T$ on the Earth. They are taken to the surface of a planet where the acceleration due to gravity... show full transcript

Worked Solution & Example Answer:A simple pendulum and a mass–spring system each have a time period $T$ on the Earth - AQA - A-Level Physics - Question 30 - 2021 - Paper 1

Step 1

Time period of the simple pendulum

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Answer

The formula for the time period of a simple pendulum is given by:

T=2πLgT = 2\pi \sqrt{\frac{L}{g}}

On the new planet, the acceleration due to gravity is rac{g}{4}. Therefore, the new time period T′T' becomes:

T′=2πLg4=2π4Lg=2TT' = 2\pi \sqrt{\frac{L}{\frac{g}{4}}} = 2\pi \sqrt{\frac{4L}{g}} = 2T

Thus, the time period of the simple pendulum on the planet is 2T2T.

Step 2

Time period of the mass-spring system

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Answer

The formula for the time period of a mass-spring system is given by:

T=2πmkT = 2\pi \sqrt{\frac{m}{k}}

Since the mass and spring constant remain unchanged when taken to the planet, the time period for the mass-spring system stays the same, which is TT.

Thus, the time period of the mass-spring system on the planet is TT.

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