- #1
jgens
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Homework Statement
The period of a mass m oscillating on a hookian spring of negligible mass.
Homework Equations
F = -kx
The Attempt at a Solution
I'm using x in place of ∆x for convienance.
F = -kx
dv/dt = -kx/m
∫vdv = -k/m∫xdx
v^2 = C - k(x^2)/m: Placing the restraint that if v = 0, x = xi
v^2 = k(xi^2)/m - k(x^2)/m
v = sqrt(k(xi^2)/m - k(x^2)/m)
t = sqrt(m/k)∫dx/sqrt(xi^2 - x^2)
t = arcsin(x/xi)sqrt(m/k). Therefore, if we allow ∆x = 0
t = arcsin(0)sqrt(m/k). Hence, if we want the time for one period:
t = 2pisqrt(m/k)
Is this correct? Thanks!