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How does the period of a pendulum vary theoretically with (a) length (b) mass of bob and (c) angular displacement?
Wiki User
∙ 7y ago
(a) directly with its square root.(b) not at all if it can be considered as a point mass which is significantly greater than the "string". Otherwise corrections are necessary.
(c) not if the angle is small. Otherwise corrections are necessary.
Wiki User
∙ 7y ago
Wiki User
∙ 6y agoFor small angular displacements, the period, t, is given by the equation,t = 2*pi*sqrt(l/g) where l is the length and g is acceleration due to gravity.
As the angular displacement increases, the equation becomes more of an approximation: at around 20 degrees, the above equation predicts a period which is 1% too short.
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How does the period of a pendulum vary theoretically with angular displacement?
In the standard derivation of pendulum characteristics, at least through high schooland undergraduate Physics, an approximation is always made that assumes a smallangular displacement.With that assumption, the angular displacement doesn't appear in the formula forthe period, i.e. the period depends on the pendulum's effective length, and isindependent of the angular displacement.
What are the factor affecting on the simple pendulum?
The factors that affect a simple pendulum are; length; angular displacement; and mass of the bong.
What 3 variables that might affect the number of cycles the pendulum makes in 15 seconds?
The length of the pendulum, the angular displacement of the pendulum and the force of gravity. The displacement can have a significant effect if it is not through a small angle.
How does a pendulums period vary with the length of its mass With Gravitational acceleration?
The length of the pendulum is measured from the pendulum's point of suspension to the center of mass of its bob. Its amplitude is the string's angular displacement from its vertical or its equilibrium position.
What are the physical parameters in the investigation of a simple pendulum?
The physical parameters of a simple pendulum include (1) the length of the pendulum, (2) the mass of the pendulum bob, (3) the angular displacement through which the pendulum swings, and (4) the period of the pendulum (the time it takes for the pendulum to swing through one complete oscillation).
How does the period of a pendulum vary theoretically with a angular displacement b mass of bob and c length?
(a) directly with its square root.(b) not at all if it can be considered as a point mass which is significantly greater than the "string". Otherwise corrections are necessary. (c) not if the angle is small. Otherwise corrections are necessary.
How does the period of a pendulum difference theoretically with length for simple pendulum?
The period is directly proportional to the square root of the length.
What affects a pendulum?
The mass of the pendulum, the length of string, and the initial displacement from the rest position.
What is the maths of period of pendulum?
For small swings, and a simple pendulum:T = 2 pi root(L/g) where T is the time for one period, L is the length of the pendulum, and g is the strength of the gravitational field.
What are the limitation of simple pendulum?
The popular formula for the period of a pendulum works only for small angular displacements. In deriving it, you need to assume that theta, the angular displacement from the vertical, measured in radians, is equal to sin(theta). If not, you need to make much more complicated calculations. There are also other assumptions to simplify the formula - eg string is weightless. The swing of the pendulum will precess with the rotation of the earth. This may not work if the pendulum hits its stand! See Foucault's Pendulum (see link). The motion of the pendulum will die out as a result of air resistance. Thermal expansion can change the length of the pendulum and so its period.
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%.
Dimension of Angular Displacement?
Angular displacement is measured in angles, usually degrees or radians. Especially when the unit radian is used, this unit is usually considered to be adimensional, since the radian is defined by the division (ratio) of two lengths: the length of an arc divided by the radius.
