Calculate the frequency of a simple pendulum, if its length is 50 cm.(Note: The acceleration due to gravity ‘g’ is 9.8 m/s2.
Question
Calculate the frequency of a simple pendulum, if its length is 50 cm.(Note: The acceleration due to gravity ‘g’ is 9.8 m/s2.
Solution
Sure, let's calculate the frequency of a simple pendulum step by step.
Step 1: First, we need to understand the formula for the frequency of a simple pendulum. The formula is:
f = 1 / (2π) * √(g / l)
where:
- f is the frequency,
- g is the acceleration due to gravity, and
- l is the length of the pendulum.
Step 2: Now, let's plug in the given values into the formula. The length l is given as 50 cm, but we need to convert it to meters because the value of g is given in m/s². So, l = 50 / 100 = 0.5 m.
f = 1 / (2π) * √(9.8 / 0.5)
Step 3: Calculate the value inside the square root first:
= 1 / (2π) * √19.6
Step 4: Now calculate the square root:
= 1 / (2π) * 4.43
Step 5: Finally, calculate the frequency f:
= 0.71 Hz
So, the frequency of the simple pendulum is approximately 0.71 Hz.
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