- #1

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several different methods and each time cant make sense of what is going on wrong

" A mass spring motion is governed by the ordinary differential

equation m(dx^2/dt^2) + b(dx/dt) + kx=F(t) , where m is the mass, b

is the damping constant, k is the spring constant, and F(t) is the

external force."

Assume the following m=1 kg, k= 16 N/m, and F(t)=0, x(0)=0, x'(0)=0.

Solve the ODE on the interval [0,20] for the following cases.

a). b=0 -no damping

b). b=2- under damping

c). b=8 - critical damping

d). b=10 - over damping

2.

Set the damping constant equal to 0, b=0, and consider an agiing spring whose spring constant depends on time as follows

k(t)=16e^-LT

Predict the motion of the mass, i.e. show time plots and phase plots and discuss your results for the following cases.

a. L=0

b. L=0.1

c. L=0.3

3.

Set b = 1/5 k=1/5 and assume a forcing F(t) = coswt,

a. Use ODE45-solver to obtain the solution curves for several values of w between .5 and 2. Plot the solutions and estimate the amplitude A of the steady response in each case.

b. Using the data from part (a) plot the graph of A vs. w. For what frequency W is the amplitude greatest?