# If your REALLY good in math then you should know this?

Okay, you know that math "experiment" when you tie the string on something that has mass and then let it swing. How is this related to math... Like... I don't get it, what is the conclusion of this?

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The link between the physics and maths is the differential

equation obtained by applying Newton's second law of

motion : F = m a (force = mass * acceleration).

You need to find the fysical forces, here

the gravity (g) and the spring (kx) with

x = displacement

a = x " (acceleration = second derivative of displacement)

so we have

m x" = g - kx

and this is a linear differential equation that can be solved

using mathematical techniques.

mx " + kx = g

try x = exp(rt), then we have

r² m + k = 0

r = sqrt(-k/m) = sqrt(k/m) i

so we have

g/k + A cos(sqrt(k/m) t) + B sin(sqrt(k/m) t)

as solution to the differential equation.

The unknown generel constants A en B can be

calculated if we have an initial condition

x(t=0) = 0, e.g.

x ' (t=0) = 0

The sin and cos give periodic solution (the swing).

Well if you swing it in a horizontal plane circle the string is tense with the centripetal force to keep the mass going in a circle.

The centripetal force = m(v^2)/r

Or you can swing it as a pendulum which has a frequency related to the length of the string. So for small angles of swing, the period of oscillation,

T = 2 pi (l/g)^(1/2)

As it swings the kinetic energy is converted to potential energy at the highest point & back again. When it is at bottom point all the energy is kinetic energy.

total energy = kinetic + potential

(m v^2)/2 = m g h , considering the two extremes.

That what you were after??????