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WOLFRAM|DEMONSTRATIONS PROJECT

Free Response in a Second-Order System

M (kg)

damping N/m/s

critical ξ

stiffness N/m

simulation time (sec)

y(0) m

0.3

y'(0) m/s

start simulation

auto y-axis scale

gridlines

test cases

case 1

underdamped

time	y( t )	ω n	ω d	ξ	T d	τ
00100	-000000	0.730	0.714	0.213	008.806	006.429
y(t) = exp(-ξ ω n t) (A cos( ω d t) + B sin( ω d t))

This Demonstration can be used to study the free response of a second-order linear system. You can vary the system parameters (mass, damping, and stiffness) and simulate the response. The analytical solution is displayed at the top of the plot for the cases of underdamping, critically damping, and overdamp. In addition, a standard physical model of mass-spring-damper is run at the same time as the response plot is updated. You can set the initial conditions for initial position and speed using the sliders. Setting the initial conditions to

y(0)=0

and

y'(0)=1

makes the response the same as the impulse response.

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