evaluate_step_response Function

public pure elemental function evaluate_step_response(wn, zeta, xs, t) result(rst)

Evaluates the response of an underdamped single-degree-of-freedom, linear system to a step function of amplitude $X_s$.

The step function response of an underdamped linear SDOF system is given as follows.

$$\ddot{x} + 2 \zeta \omega_n \dot{x} + \omega_n^2 x = \frac{F(t)}{m}$$

$$\frac{x(t)}{X_s} = 1 - e^{-\zeta \omega_n t} \left( \frac{\zeta \omega_n}{\omega_d} \sin{\omega_d t} + \cos{\omega_d t} \right)$$

where,

$$\omega_d = \omega_n \sqrt{1 - \zeta^2}$$

and

$$X_s = \frac{F}{k}$$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	wn	The resonant frequency, in rad/s.
real(kind=real64),	intent(in)			::	zeta	The damping ratio.
real(kind=real64),	intent(in)			::	xs	The amplitude of the step input.
real(kind=real64),	intent(in)			::	t	The point in time at which to evaluate the response (units = s).

Return Value real(kind=real64)

The step response.

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