Okay, so my equation and the initial conditions are correct.
How do I go about getting γ and k?
Would I get constants (numbers) or would it be a function of something?
With only knowing C1 and C2, I have no idea how to proceed.
Thank you for your reply.
In my text, I have y(t) = c1e^(λ1t) + c2e^(λ2t) as an over-damped case,
y(t) = c1e^(λt) + c2te^(λt) as a critically-damped case,
and y(t) = (A+B)e^(rt) as an underdamped case.
I'm wondering if I made a mistake somewhere with the initial conditions.
It...
Homework Statement
A spring and dashpot system is to be designed for a 32lb weight so that the overall system is critically damped.
(a) How must the damping constant γ and spring constant k be related?
(b) Assume the system is to be designed so that the mass, when given an initial velocity of...
Homework Statement
Solve the IVP, \frac{1}{4}y'' + 16y = 0
y(0)=\frac{1}{4}
y'(0)=0
Answer is given... y(t) = \frac{1}{4}cos 8t
Homework Equations
The Attempt at a Solution
This has the characteristic equation \frac{1}{4} \lambda^2 +16\lambda=0
Solving for lambda, I got...
Hi. Thanks for your reply.
I'm doing another question like this and this one has a variable "t" in it.
Q) 2e^(i*\sqrt{2}*t) => Write in Standard Form
Using Euler's Equation, I have
-> 2*(cos \sqrt{2}*t + i sin \sqrt{2} t)
How do I simplify this? Since the angle \sqrt{2} is not...
Thank you for your reply.
I'm not a math genius (as you could probably tell) and imaginary numbers, especially tend to throw me off.
But your equations help a lot.
Frankly, I've never seen this equation. z = re^(i*theta) = r (cos (theta) + i sin (theta).
Anyway, thanks again for your...
Firstly, thanks for your reply.
And yes... Eular's equation says...
e^(i*beta*t) = cos (beta*t) + i*sin (beta*t)
But I wasn't sure how to use this equation since t is missing in the question...
Homework Statement
Write 2*EXP(i*pi/3) in the form \alpha + i\beta
Answer is given = 1 + sqt(3)i
Homework Equations
The Attempt at a Solution
I'm supposed to turn this exponential form of imaginary number into a standard form in order to solve an ODE.
I have no idea how they got 1+sqt(3)i...