- #1
ConnorM
- 79
- 1
Homework Statement
I uploaded the question as a picture and attached it.
Homework Equations
Unit step function -
[itex]u_c (t) =
\begin{cases}
1 & \text{if } t \geq c \\
0 & \text{if } t < c
\end{cases}[/itex]
Impulse function -
[itex] δ(t) = \displaystyle\lim_{Δ\rightarrow 0} δ_Δ (t)[/itex]
Multiplication Property for Impulse function -
[itex] f(t)⋅δ(t - t_d) = f(t_d)⋅δ(t - t_d)[/itex]
*A function [itex]f(t)[/itex] becomes a value [itex]f(t_d)[/itex]*
The Attempt at a Solution
(a and b)
I have determined that both of the transfer functions are the same,
[itex] H(s) = V(s)/F_{p / w}(s) = {\frac{1}{75s + 0.0046}} [/itex]
(c)
The Laplace transform of the impulse function is 1 so,
[itex] V(s) = {\frac{1}{75s + 0.0046}} [/itex]
[itex] v(t) = {\frac{1}{75}} e^{{\frac{-0.0046}{75}}t} [/itex]
(d)
The Laplace transform of the unit step function is 1/s so,
[itex] V(s) = {\frac{1}{s(75s + 0.0046)}} [/itex]
[itex] v(t) = 217.391 - 217.391 e^{{\frac{-0.0046}{75}}t} [/itex]
***Am I right up to this point?***
(e)
[itex]f_{wind} (t) =
\begin{cases}
4.5 & \text{if }1 \geq t < 10 \\
0 & \text{otherwise,}
\end{cases}[/itex]
Does that mean that from 1 -> 10 there is a constant force of only 4.5N? That just seems negligible compared to the force applied by the skaters pushes.
[itex] f(t) = f_{wind}(t) + 1160δ(t-4) + 935δ(t-6) + 708δ(t-7.8) [/itex]
Not quite sure how to model this!