Arbitrary Excitations | Energy and Damping | Alison
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Energy and Damping

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Energy and DampingWelcome back to the Structural Dynamics course. In the last few lectures we have been learning about harmonic vibrations, that is the vibrations of a single degree of freedom system under harmonic forces. In the last week we also saw that, any periodic force can be represented in terms of multiple harmonic forces. So, a response to a periodic force of a linear system is equal to the sum of the responses to it is harmonics. Now, let us see how energy is balanced during harmonic vibrations.(Refer Slide Time: 00:58)Now, let us see the energy input to a single degree of freedom system under harmonic force. This is the equation of motion of a single degree of freedom system; we have mass damping and stiffness. So, this is the spring force, this is the damping force, this is the inertia force and the sum is equal to the harmonic force acting on the system.We also learned that this system has two types of response, transient response and steady state response. Transient response decays in time so, after some time only steady state response will be dominant and the steady state response is equal to x naught sin omega t minus phi. So, we learnt the expression for x naught that is the amplitude of the steady state response. So, we have derived this expression and this p naught by k is equivalent to the static response that is if this force was a static force the response would have been p naught by k that is force by stiffness.x(t) = x0

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