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both...since the weight will act at a downward force and the string will have tensile force (aka tension) that is directed away from the weight and towards the centre of the pendulum....the value of both these forces will determine how fast the pendulum swings

2007-09-22 12:24:07 · answer #1 · answered by ? 3 · 0 1

The number of times a pendulum swings (its frequency) happens to only be related to the length of the string and not the mass on the string. Essentially a pendulum is converting gravitational potential energy into kinetic energy. Lets take a look at the motion of a pendulum in polar coordinates.

Potential energy: U = m g L cos(p)

Kinetic energy: T = 1/2 m L^2 p'^2

Our Lagrangian for motion is:

L = T - U = 1/2 m L^2 p'^2 - m g L cos(p)

If we wish to find in equation of motion we can use Lagrane's equation.

d/dt ( dL/dp') - dL/dp = 0

d/dt (m L^2 p') + m g L sin(p)= 0, if p is a small angle sin(p) = p

m L^2 p'' + m g L p= 0, mass cancels out

p'' + g/L p = 0

This is a second-order homogeneous differential equation which happens to be the solution to a harmonic oscillator with angular frequency sqrt (g/L).

This would mean that the frequency of a pendulum is:

2 pi sqrt(g/L) = f

This only depends on the acceleration of gravity (a constant) and the length of the string.

2007-09-22 19:39:06 · answer #2 · answered by msi_cord 7 · 1 1

IDK I'm confused

2007-09-22 20:59:46 · answer #3 · answered by nikki 3 · 0 0

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