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If a pendulum's length is 2.00 m and ag = 9.80 m/s, how many complete oscillations does the pendulum make in 5.00 min?​

User Di
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1 Answer

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20 votes

Answer:

Number of oscillation = 106 oscillations

Step-by-step explanation:

Given the following data;

  • Length = 2 m
  • Acceleration due to gravity, g = 9.8 m/s²
  • Time = 5 minutes

To find how many complete oscillations the pendulum makes in 5.00 min;

First of all, we would determine the period of oscillation of the pendulum using the following formula;


T = 2 \pi \sqrt{(l)/(g)}

Where;

  • T is the period.
  • l is the length of the pendulum.
  • g is acceleration due to gravity.

Substituting into the formula, we have;


T = 2 * 3.142 \sqrt{(2)/(9.8)}


T = 6.284 √(0.2041)


T = 6.284 * 0.4518

Period, T = 2.84 seconds

Next, we would determine the number of complete oscillation in 5 minutes;

We would have to convert the time in minutes to seconds.

Conversion:

1 minutes = 60 seconds

5 minutes = X seconds

Cross-multiplying, we have;

X = 5 * 60 = 300 seconds

Mathematically, the number of oscillation of a pendulum is given by the formula;


Number \; of \; oscillation = \frac {Time}{Period}

Substituting into the formula, we have;


Number \; of \; oscillation = \frac {300}{2.84}

Number of oscillation = 105.63 ≈ 106 oscillations

Number of oscillation = 106 oscillations

User Gianfranco
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