What change would double the period of a pendulum?

• A. Doubling the mass of the bob
• B. Doubling the amplitude of the pendulum's swing
• C. Quadrupling the length of the pendulum
• D. Quadrupling the mass of the bob

Answer: (C)

The period of a simple pendulum, which is the time it takes to complete one full oscillation, is determined primarily by its length and the acceleration due to gravity. The formula for the period ( T ) of a pendulum is given by:

[

T = 2\pi \sqrt{\frac{L}{g}}

]

where ( L ) is the length of the pendulum and ( g ) is the acceleration due to gravity.

To double the period ( T ), we can derive the necessary change based on the formula. If we want ( T' = 2T ), we substitute into the equation to find out how ( L ) must change:

[

2T = 2\pi \sqrt{\frac{L'}{g}}

]

Squaring both sides gives:

[

(2T)^2 = 4T^2 = 4\pi^2 \frac{L'}{g}

]

Since we know from the original formula that:

[

T^2 = \frac{4\pi^2 L}{g}

]

we can set those equal:

[

4T^2 = 4\pi^2 \frac{L