Hello everyone, I am actually a mechanical engineering major at the University of Texas, but I thought I'd ask you kind folks for help with this problem. I apologize in advance for this being difficult to read because I don't know how to type many of these symbols.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

"The response of the mass-spring-damper due to a hammerblow F at t=to is described by:

m*ydotdot + c*ydot + k*y = F(lowercase delta (t-to)).

For a particular system: ydotdot+3*ydot+2y = (lowercase delta(t-1)).

a. Using Laplace transforms, determine the mass displacement, y(t) for a system that was initially at rest. Plot y(t) for 0 <= t <= 6.

b. Next, determine and plot the force on the mass Fm(t) for 0 <= t <= 6. Neglect the gravitational force mg as it is constant and hence does not affect the dynamics of the system.

2. Relevant equations

See above--ydot is the first differentiation of y, ydotdot is the second.

3. The attempt at a solution

I took the Laplace transforms of both sides, and ended up with:

[s^2*Y(s) - s*yo - ydoto] + 3[s*Y(s)-yo]+2Y(s)=L{lowercase delta[t-1]}.

For part a, I assumed that since the system was initially at rest, y(o)=0, and ydot(o)=0.

I then solved for Y(s), and rearranging the info, I got:

Y(s) = L{lowercase delta[t-1]}/(s^2+3*s+2)+(s+1)yo/(s^2+3*s+2)+ydoto/(s^2+3s+2).

Assuming that yo=0 and ydoto=0, the last two terms should equal zero, leaving you with Y(s)= L{lowercase delta[t-1]}/(s^2+3*s+2). You could simplify the bottom term to (s+2)*(s+1), but I'm not sure how to proceed from there.

Thanks for your help!

--Jeremy

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# Homework Help: Using Laplace transforms to solve mass-spring-damper systems

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