EXERCISE 10.6. A Brownian particle of mass m is attached to a harmonic spring with force constant,
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EXERCISE 10.6. A Brownian particle of mass m is attached to a harmonic spring with force constant, k, and is driven by an external force, F(t). The particle is constrained to move in one dimension. The Langevin equation is
where (k/m), y is the friction constant, and (t) is a Gaussian white noise with zero mean. Then equation of motion of the average position, (x(t)), in the presence of the external force, F(t), is
(a) Compute and plot the linear response function, K(t), where (x(t)) = K(t-)F(t)dr.
(b) Compute the total energy absorbed for the case of a driving force, F(t) = Fo8(t) [10].
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