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Diff Eq 3.6

 

<== Differential Equations
Number Question Answer
See the work
1.

This is an example of an Undamped Forced Oscillation where the phenomenon of Beats Occurs.

Find the solution of the initial value problem:

x'' +  7.84 x =  5 \cos(3t) x'' +  3.24 x =  4 \cos(2t), , \quad x(0)=x'(0)=0

x(t) = ___________

Graph the solution to confirm the phenomenon of Beats.

What is the period of the slow oscillation?
Period = _________

x(t)=

Period = 31.4
The work

Point Cost: 3
2.

This is an example of an Undamped Forced Oscillation where the phenomenon of Pure Resonance Occurs. 

Find the solution of the initial value problem:

x'' +  9 x =  24 \sin(3 t) , \quad x(0)=x'(0)=0

x(t) =  
x(t)=
The work

Point Cost: 3
3.

The solution to the Initial value problem

x'' + 2 x' + 82 x = 6 \cos(4 t), \quad x(0)=0, x'(0)=0
is the sum of the steady periodic solution x_{sp} = C \cos(\omega t - \alpha) and the transient solution x_{tr}. Find both x_{sp} and x_{tr}
x_{sp} =  
x_{tr} = 

x_{sp} =
x_{tr} =e^-t(-99/1105cos(9t)-49/3315sin(9t))
The work

Point Cost: 3