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tjr39
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[SOLVED] Lightly damped spring system Q
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)
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.
Homework Statement
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)
Homework Equations
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.