Home
Back
Formula Used:
| From: | To: |
The formula calculates the horizontal distance moved by a pendulum based on the length of the plumb line and the tilting angle of the body. This is derived from trigonometric principles in right triangle geometry.
The calculator uses the formula:
Where:
Explanation: The tangent function relates the opposite side (horizontal distance) to the adjacent side (plumb line length) in a right triangle formed by the pendulum's position.
Details: Accurate calculation of pendulum movement is crucial for various applications including physics experiments, engineering measurements, and mechanical system design where pendulum motion is involved.
Tips: Enter the length of plumb line in meters and the tilting angle in radians. Both values must be positive numbers (length > 0, angle ≥ 0).
Q1: Why use radians instead of degrees for the angle?
A: Trigonometric functions in mathematical calculations typically use radians as the standard unit. Most programming languages and calculators expect angle inputs in radians.
Q2: What is the range of valid angles for this formula?
A: The formula works for angles from 0 to π/2 radians (0° to 90°). Beyond π/2 radians, the tangent function becomes undefined or negative, which may not represent physical pendulum movement.
Q3: Can this formula be used for large angle pendulum movements?
A: This formula assumes small angle approximation and may become less accurate for large angles where the pendulum motion becomes non-linear.
Q4: How does plumb line length affect the distance moved?
A: The distance moved is directly proportional to the length of the plumb line. Longer pendulums will move greater distances for the same angle of tilt.
Q5: What are practical applications of this calculation?
A: This calculation is used in seismology for pendulum seismometers, in construction for measuring inclinations, and in various mechanical systems that use pendulum principles.