# Homework Help: Lightly damped spring system Q

1. Mar 25, 2008

### tjr39

[SOLVED] Lightly damped spring system Q

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.

2. Mar 25, 2008

### pam

Also find the initial velocity by d\psi/dt.