a simple pendulum has a period of 2.0s and an amplitude of swing 5.0cm.calculate the maximum magnitude of the acceleration of the bob
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9.8+100*.120
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To calculate the maximum magnitude of the acceleration of the bob in a simple pendulum, we can use the formula for the acceleration of an object undergoing simple harmonic motion:
a_max = ω^2 * A
where:
a_max is the maximum magnitude of the acceleration,
ω is the angular frequency (2π divided by the period), and
A is the amplitude of swing.
Given:
Period (T) = 2.0 s
Amplitude (A) = 5.0 cm
First, let's convert the amplitude from centimeters to meters:
Amplitude (A) = 5.0 cm = 0.05 m
Next, calculate the angular frequency (ω):
ω = 2π / T
ω = 2π / 2.0
ω = π rad/s
Now, substitute the values into the formula for acceleration:
a_max = ω^2 * A
a_max = (π)^2 * 0.05
a_max ≈ 0.4907 m/s^2
Therefore, the maximum magnitude of the acceleration of the bob in the simple pendulum is approximately 0.4907 m/s^2.