Simple Pendulum Calculator

The mass suspended from a rod is referred to as a simple pendulum. The pendulum means the position is defined as a straight vertical line passing through the fixed position.

The following are the most essential factors of the simple pendulum

• The length of the pendulum is the distance between the centre of mass and the point of suspension, and it is represented by L.
• The oscillatory motion of a simple pendulum is periodic to and fro motion of the pendulum, and the equilibrium is the mid-point of the oscillation.
• The time it takes the pendulum to complete one full oscillation is known as the time period of the simple pendulum, and it is represented by the letter T.
• The distance travelled by a simple pendulum from one side to the equilibrium position is its amplitude.

The following are the formulas for calculating the simple pendulum period and frequency T = 2π × √(L/g), f = 1/T

• Where, T = time period of the pendulum
• f = frequency of the pendulum
• L = length of the pendulum
• g = acceleration due to gravity

Here are the easy guidelines for calculating the simple pendulum time period and frequency.

• Step 1: Calculate the gravitational acceleration and the length of the pendulum.
• Step 2: Divide the length by gravity's acceleration and take the square root of the result.
• Step 3: The time period is calculated by multiplying the value obtained in the previous step by 2π.
• Step 4: The frequency of the pendulum is the reciprocal of the time period.

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The following is the procedure how to use the simple pendulum calculator

• Step 1: In the appropriate input fields, enter the length (L), gravity acceleration (g), and x for the unknown.
• Step 2: To calculate the time period, click the "Calculate the Unknown" button.
• Step 3: Finally, the output field will show the value of x.

Question 1:Find the time period and frequency of a simple pendulum with a length of 30 metres.

Solution:

Given: L = 30 m

g = 9.8 m/s

Time Period T = 2π × √(L/g)

T = 2π × √(30/9.8)

= 2π × √(30/9.8)

= 2π × √(3.0612)

= 10.99

frequency f = 1/T

f = 1/10.99

= 0.09

As a result, the simple pendulum's average period and frequency are 10.99 seconds and 0.09 oscillations per second, respectively.

1. What are the three simple pendulum laws?

The three laws of a pendulum are as follows

• A pendulum's time of oscillation is independent of its amplitude when its length is constant.
• The shape, size, and material of a simple pendulum of constant length have no bearing on the period of oscillation.
• A pendulum's time period is related to the square root of the length of a simple pendulum.

2. What is the formula for calculating the pendulum's length?

L = (T²g)/(4π²) is the formula for calculating the length of a simple pendulum.

3. What is the pendulum's oscillation?

Oscillation refers to a pendulum that swings from one extreme to the other before returning to its original point.

4. How do you calculate a pendulum's kinetic energy?

The kinetic energy would be KE= 1/2mv^2, where m is the pendulum's mass and v is the pendulum's speed. The pendulum is briefly immobile at its highest point.

5. What are the uses of a simple pendulum?

The clock, wrecking ball, ballistic pendulum, bowling ball, Foucault's pendulum, and metronome are all real-time uses of a simple pendulum.