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Given the neural excitation,

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body u(t)

, shown below, derive an expression for and plot the muscle activation,

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body a(t)

, as a function of time. Label any critical points in your graph. Assume that the time constant for activation is 0.12 seconds and the time constant for deactivation is 0.24 seconds.

Feel free to use either the excitation-activation excitation–activation dynamics ODE from your textbook , or the ODE shown below to do your calculations.

Excitation-Activation Dynamics Excitation–activation dynamics ODE: 

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\frac{da(t)}{dt} + \left[ \frac{1}{\tau_{act}} \cdot \Big( \beta + \left(1-\beta\right) u(t) \Big) \right] \cdot a(t) = \frac{u(t)}{\tau_{act}}

where 

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body --uriencoded--\beta = \frac%7B\tau_%7Bact%7D%7D%7B\tau_%7Bdeact%7D%7D

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excerpt-include S4.1 Excitation-activation Excitation–activation dynamics S4.1 Excitation-activation Excitation–activation dynamics