What is the length of a simple pendulum that oscillates in 2 seconds?

What is the length of a simple pendulum that oscillates in 2 seconds?

• A. 2 m
• B. 4 m
• C. 6 m
• D. 8 m

Answer: (B)

To determine the length of a simple pendulum that oscillates in 2 seconds, we can use the formula for the period of a simple pendulum: \[ T = 2\pi \sqrt{\frac{L}{g}} \] where \( T \) is the period of the pendulum (the time taken to complete one full oscillation), \( L \) is the length of the pendulum, and \( g \) is the acceleration due to gravity, approximately \( 9.81 \, m/s^2 \). In this case, we know the period \( T \) is 2 seconds. We can rearrange the formula to solve for \( L \): \[ L = \frac{g T^2}{4\pi^2} \] Substituting the known values into the equation: 1. Substitute \( T = 2 \) seconds: \[ L = \frac{9.81 \times (2)^2}{4\pi^2} \] 2. Calculating \( (2)^2 \) gives 4, so: \[ L = \frac{9.81 \times 4}{4\pi^2} \] \

To determine the length of a simple pendulum that oscillates in 2 seconds, we can use the formula for the period of a simple pendulum:

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

where ( T ) is the period of the pendulum (the time taken to complete one full oscillation), ( L ) is the length of the pendulum, and ( g ) is the acceleration due to gravity, approximately ( 9.81 , m/s^2 ).

In this case, we know the period ( T ) is 2 seconds. We can rearrange the formula to solve for ( L ):

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

Substituting the known values into the equation:

1. Substitute ( T = 2 ) seconds:

[ L = \frac{9.81 \times (2)^2}{4\pi^2} ]

2. Calculating ( (2)^2 ) gives 4, so:

[ L = \frac{9.81 \times 4}{4\pi^2} ]

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