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
Question 30
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=2πgL
On the planet, the acceleration due to gravity is 4g, so we substitute this into the formula:
T′=2π4gL=2πg4L=2⋅2πgL=2T
Thus, the time period of the simple pendulum on the planet is 2T.
Step 2
Time period of the mass–spring system
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Answer
The time period of a mass-spring system is given by:
T=2πkm
This formula is independent of gravity, so the time period remains the same. Therefore, the time period of the mass-spring system on the planet is also T.
