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Summary: Math 308, Matlab assignment 3
due October 21 in class
1. A mass of 1 kg is attached to an (idealized) spring with the spring constant 100 N/m2
and zero
damping. The mass is at rest at the equilibrium position of the spring. Then, starting at time 0, an
external force cos 9t is applied to the mass.
(a) Use dsolve to find the position of the mass as a function of time. Write down the formula
in your report.
(b) Use ezplot to plot your solution on the interval [-10, 10]. If you do this correctly, you
should observe the phenomenon of "beats". It is encountered in practice with speakers that
have feedback.
2. A mass of 1 kg is attached to a spring with the spring constant 5 N/m2
and the damping constant
2 N/m. The mass is at rest at the equilibrium position of the spring. Then, starting at time 0, an
external force cos t is applied to the mass.
(a) dsolve does not work on this problem (try it if you want), so we will have to use a numer-
ical solver ode45. First, we need to write the second order ODE
my + by + ky = F(t)
as a system of two first-order ODE
u1 = u2,
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