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**[SOLVED] Lightly damped spring system Q**

**1. 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;

[tex]\Psi(t)=Ce^{-\frac{\lambda}{2}t}Cos(\omega_{r}t+\pi)[/tex]

**2. Homework 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,

[tex]\Psi(0)=Ce^{-\frac{\lambda}{2}*0}Cos(\omega_{r}*0+\pi)[/tex]

Which simplifys to [tex]\Psi(0)=-C[/tex] (as [tex]e^{0}=1[/tex] and [tex]Cos(\pi)=-1[/tex])

So is my answer just the spring should be stretched by aplitude C to give above equation of displacement? Thanks.