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e^(i Pi)+1=0
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Homework Statement
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A mass-spring system is oscillating with an amplitude of 10.0 cm. What is the speed of the mass at a location where the kinetic energy of the mass and the potential energy of the spring are equal?
I want to know if it's possible to solve for just a number, that is, not in terms of k and m. Also if my answer is right as it is. Thanks.
Homework Equations
The Attempt at a Solution
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Force equals ma and also -kx
ma = -kx
ma+kx = 0
x''+(k/m)x = 0
Solve the differential equation, set x(0) = 0 and set the amplitude to 0.1 (in meters) to yield
x(t) = 0.1sin(√[k/m]t)
Differentiate to find v(t) and sub them into the equation
(1/2)mv2 = (1/2)kx2
I find t = π/4 and v(π/4) = -0.05√(2k/m)