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In control theory the impulse response is the response of a system to a Dirac delta input. This proves useful in the analysis of dynamic systems; the Laplace transform of the delta function is 1, so the impulse response is equivalent to the inverse Laplace transform of the system's transfer function.
In physics, action is a scalar quantity that describes how the balance of kinetic versus potential energy of a physical system changes with trajectory. Action is significant because it is an input to the principle of stationary action , an approach to classical mechanics that is simpler for multiple objects. [ 1 ]
An example response of system to sine wave forcing function. Time axis in units of the time constant τ. The response damps out to become a simple sine wave. Frequency response of system vs. frequency in units of the bandwidth f 3dB. The response is normalized to a zero frequency value of unity, and drops to 1/√2 at the bandwidth.
t 1 and t 2 are times when the impulse begins and ends, respectively, m is the mass of the object, v 2 is the final velocity of the object at the end of the time interval, and; v 1 is the initial velocity of the object when the time interval begins. Impulse has the same units and dimensions (MLT −1) as momentum.
The impulse response can be computed to any desired degree of accuracy by choosing a suitable approximation for δ, and once it is known, it characterizes the system completely. See LTI system theory § Impulse response and convolution. The inverse Fourier transform of the tempered distribution f(ξ) = 1 is the delta function.
If a system initially rests at its equilibrium position, from where it is acted upon by a unit-impulse at the instance t=0, i.e., p(t) in the equation above is a Dirac delta function δ(t), () = | = =, then by solving the differential equation one can get a fundamental solution (known as a unit-impulse response function)
Because of its many applications in information theory, physics and engineering there exist alternative names for specific linear response functions such as susceptibility, impulse response or impedance; see also transfer function. The concept of a Green's function or fundamental solution of an ordinary differential equation is closely related.
As described by the third of Newton's laws of motion of classical mechanics, all forces occur in pairs such that if one object exerts a force on another object, then the second object exerts an equal and opposite reaction force on the first. [1] [2] The third law is also more generally stated as: "To every action there is always opposed an ...