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**1. Homework Statement**

A linear harmonic oscillator is subject to friction(stokes). The Oscillator gets an Impulse at the time t = 0 at the rest position. What is the equation of motion for the time interval 0 - t0?

**2. Homework Equations**

Friction force: Fr = -a * x'(t); a = constant (stokes friction)

**Impulse: F(t) = m *v0 / t0**(for 0 <= t <= t0)

k = spring constant

m = mass

x(t = 0) = 0 (rest position at the time t = 0)

x'(t = 0) = 0 (velocity at the time t = 0 is zero)

**3. The Attempt at a Solution**

I have a little trouble with the impulse here. My attempt at a solution was this:

m*x'' = -k*x - a*x' + m*v0/t0 ==>

**x'' + (a/m)*x' + (k/m)*x = v0 / t0**

But my book claims that the equation really goes like this:

x'' + (a/m)*x' + (k/m)*x = v0 / t0 * (1/m)

Does somebody know why I am wrong and the book is right? I don't understand it, because I thought I needed a force(respectively acceleration) in above equation of motion. How does

**v0 / t0 * (1/m)**fit into the equation, doesn't it have the wrong units?

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