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- 18 September 2008
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I have a maths question:
A physical mass-spring system is modelled by the second-order differential equation
M
d2y
dt2 + 2
dy
dt
+ ky = 0
where k is the spring constant,
is the damping coefficient, and M is the mass.
(i) Show that, if
2 < kM, the general solution to this system is
y(t) = e− t (Acos( t) + B sin( t))
and find expressions for and in terms of
, k, and M.
(ii) Graph the motion of the system for the initial conditions y(0) = 1, y′(0) = 0.
(iii) What is the period of the oscillation? In the limit that
! 0, what happens
to the period if the mass M is doubled?
I suggest you try http://www.wolframalpha.com
You will have to play with it a bit so that you can express the equation in a manner that Wolfram Alpha understands. But it should be able to solve most of what you are asking as well as graph the equation.
Check some of the examples on that website to find out its capabilities.
