PURPOSE: To show the transient response.
DESCRIPTION: Use a driven Shive wave machine with one end clamped. The fundamental frequency is nice and low, at .305 hertz. When the driver is applied at the fundamental it takes more than 30 seconds for the transient response to climb into the steady state response. The transient response shows a linear increase in the amplitude of the oscillations up to the steady state. But, when the frequency of the driver is mistuned slightly off resonance, the transient response is not linear. Instead, it oscillates with large beats that first build and then fade away without obtaining the steady state response.
References:
AJP 59 (5), May 1991, pp. 398 Investigations of driven harmonic oscillations in the computerized student lab.
Baierlein's "Newtonian Dynamics" p 56-58 you can find a little discussion on the transient solutions. He mentions it takes on the order of 10 tau where tau is the damping time to reach the steady state.
EQUIPMENT: Shive wave machine, driver, end clamp.
Updated by Jun Qi in 3/24/2000