Recent content by VeganGirl

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...

Ohhh that's where I went wrong. Thanks guys!

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...

Thanks everyone! You guys have been a great help! :smile:

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... Euler'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...