tjr39
Mar25-08, 07:16 PM
1. The problem statement, all variables and given/known data
Consider a lightly damped mass-on-a-spring vibrational system. How should motion be initiated so that the amplitude of the spring is given by;
\Psi(t)=Ce^{-\frac{\lambda}{2}t}Cos(\omega_{r}t+\pi)
2. Relevant equations
3. The attempt at a solution
I don't really know what is being asked "how should motion be initiated". Anyways I tried finding the solution at t=0,
\Psi(0)=Ce^{-\frac{\lambda}{2}*0}Cos(\omega_{r}*0+\pi)
Which simplifys to \Psi(0)=-C (as e^{0}=1 and Cos(\pi)=-1)
So is my answer just the spring should be stretched by aplitude C to give above equation of displacement? Thanks.
Consider a lightly damped mass-on-a-spring vibrational system. How should motion be initiated so that the amplitude of the spring is given by;
\Psi(t)=Ce^{-\frac{\lambda}{2}t}Cos(\omega_{r}t+\pi)
2. Relevant equations
3. The attempt at a solution
I don't really know what is being asked "how should motion be initiated". Anyways I tried finding the solution at t=0,
\Psi(0)=Ce^{-\frac{\lambda}{2}*0}Cos(\omega_{r}*0+\pi)
Which simplifys to \Psi(0)=-C (as e^{0}=1 and Cos(\pi)=-1)
So is my answer just the spring should be stretched by aplitude C to give above equation of displacement? Thanks.