Forced Vibrations

Abstract

IN his letter on the above subject in NATURE of June 27, Prof. Perry examines some typical dynamical and electrical solutions of the equation (D² + 2kD + n²)x = A cos pt … (1) with special reference to the critical case of maximum amplitude of the forced vibration; he shows that in all the cases examined the critical value of p which excites maximum response is either n or □n² – 2k², while the frequency of the free damped vibration is given by □n² – k², and concludes that the usual statement is not correct that for maximum response “the forcing influence ought to be in tune with the natural frequency of the system.” But is it usual to define the natural frequency of the system as □n² – k²? The term is ordinarily employed, like the German Eigenfrequenz, to designate the natural undamped frequency of the system, and, interpreted in this sense, the statement to which Prof. Perry objects is, with certain limitations, quite correct.