- #1
gob71
- 3
- 0
I am new to MATLAB and need help with a problem. we have tried
several different methods and each time can't 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?
several different methods and each time can't 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?