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Using some basic properties from physics and some small angle approximations, one can quickly arrive at the formula
T=2π√(L/g)
Where T is the period of a pendulum in seconds, L is its length in meters, and g is the acceleration due to gravity (9.81m/s²). If you square both sides of this equation, you can quickly derive that
T²=4π²*L/g
Then, if you rearrange this so that L is alone on the left hand side, you will find that
L=g*T²/(4π²)
The slope of this line is everything that is multiplying the T² term, or just g/(4π²).
What else can I help you with?
Why does the slope of the period vs root of pendulum length 2.01?
The slope of the period vs. the square root of the pendulum length being approximately 2.01 suggests that the relationship between the period (T) and the length (L) of the pendulum follows the formula (T = 2\pi\sqrt{\frac{L}{g}}), where (g) is the acceleration due to gravity. This indicates that the period is directly proportional to the square root of the length. The value of 2.01 may reflect experimental errors or approximations in the measurement of (g) or the pendulum's length, but it is close to the theoretical value of (2\pi), validating the relationship.
What is the relationship between the period and the lengthof a pendulum using logarithms?
The relationship between log(period) and log(length) is linear, with slope 0.5 and intercept log(2*pi/sqrt(g))
How do you find the length of a leg on a right triangle when one leg and the slope of the hypotenuse is given?
Use tangent. Your equation will be tan(slope of hypotenuse) = opposite side / adjacent side. it's easier if you just do A squared plus b squared equals c squared. Then subtitute the numbers gived in.
What kind of graph would result if period T were graphed as a function of the square root of the length?
If period ( T ) is graphed as a function of the square root of the length (( \sqrt{L} )), the resulting graph would be a straight line. This is because, according to the formula for the period of a simple pendulum, ( T = 2\pi \sqrt{\frac{L}{g}} ), where ( g ) is the acceleration due to gravity. The relationship shows that ( T ) is directly proportional to ( \sqrt{L} ), indicating a linear relationship with a slope of ( 2\pi / \sqrt{g} ).
How do you figure out the IMA of a inclined plane?
length of slope/ height of slope
What is the relationship between the period and the lengthof a pendulum using logarithms?
The relationship between log(period) and log(length) is linear, with slope 0.5 and intercept log(2*pi/sqrt(g))
What formula is radical radius squared plus height squared?
It is the length of the slope of a right cone.
How do you find the length of a leg on a right triangle when one leg and the slope of the hypotenuse is given?
Use tangent. Your equation will be tan(slope of hypotenuse) = opposite side / adjacent side. it's easier if you just do A squared plus b squared equals c squared. Then subtitute the numbers gived in.
What kind of graph would result if the period of the pendulum T were graphed as a function of the square root of the length of the pendulum?
With a simple pendulum, provided the angular displacement is less than pi/8 radians (22.5 degrees) it will be a straight line, through the origin, with a slope of 2*pi/sqrt(g) where g is the acceleration due to gravity ( = 9.8 mtres/sec^2, approx). For larger angular displacements the approximations used in the derivation of the formula no longer work and the error is over 1%.
What does the slope of an acceleration-position graph indicate?
Meters/seconds squared
How do you figure out the IMA of a inclined plane?
length of slope/ height of slope
How do you find area of a right triangle with leg having a length of 6 and l?
The Following Formula Is used to determine the area of any triangle. "Height" multiplied by "BASE" divided by two = area, more simply (Height x Base)/2=Area So in this Equation (6x1)/2=3 which is the area. With the length 6 and the length 1 being at a 90 degree angle With right triangles "only" you can determine the length of the slope using Triangulation Also known as the Pythagorean Theorem ( "a" squared x 'B' squared = "c" squared
Where is acceleration represented on a distance verses time squared graph?
In general, nowhere, because acceleration is the second derivative of distance with respect to time. However, in the special case of a constant acceleration, the acceleration will be twice the slope of the line, since distance = 0.5 * time squared.
What is a road on a slope?
When determining the measurement of slope on a road, the equations are for grade (gradient). The formula is grade = (rise ÷ slope length) * 100
What does the slope of a wavelength vs period graph tell you?
The slope of a wavelength vs period graph represents the speed of the wave. A steeper slope indicates a higher speed, while a gentler slope indicates a slower speed.
What is a road on a slope called?
When determining the measurement of slope on a road, the equations are for grade (gradient). The formula is grade = (rise ÷ slope length) * 100
What is the slope of the tangent line at x squared plus 2x?
Differentiate term by term. d/dx[X2 + 2X) = 2X + 2 slope(m) = 2 ------------------
