A viscous dashpot dε/dt= µσ is connected in series with a non-linear spring σ= Eε-(aε)2 where µ, a and E are constants. Determine the relaxation behavior for the model (ε as a function of σ). Draw the relaxation behavior for the non linear model (σ as a function of t) in a plot.
A viscous dashpot dε/dt= µσ is connected in series with a non-linear spring σ= Eε-(aε)2 where µ, a and E are constants. Determine the relaxation behavior for the model (ε as a function of σ). Draw t...
Harmonic response of the Maxwell element The Maxwell element for modeling a viscoelastic system treats it as a spring and a viscous dashpot connected in series as shown in the diagram below. The red arrows indicate the direction that the stress is applied. E and η are the Young's modulus of the spring and the viscosity of the dashpot component, respectively. Both parameters are real constants and characterize the model completely. dashpot spring (a) Show that the time rate of...
Please ignore part abc
4. Suppose that (X1, Yİ), , (XN,Yv) denotes a random sample. Let Si = a + bX, T, e+ dy, where a, b, c and d are constants. Let X ΣΧ, and σ2-NL Σ(x,-x)2, with the analogous expressions for y S, T. Let σΧΥ-ΝΤΣ (Xi-X)(X-Y), and let P:XY ƠXY/(ƠXƠY), with the analogous expressions for S, T. (a) Show that σ bbe (b) Show that ớsı, d ớx (c) Show that psT ST (d) How do the...
Introduction Many doors in public places are fitted with simple and inexpensive mechanisms that are designed to close the doors while reducing the slamming force to a minimum. Figure 1 Figure 1 depicts one such mechanism while Figure 2 provides a schematic description. The spring is mounted in order to push the door back to close once it is opened. The role of the hydraulic dashpot is to provide a viscous force that will prevent the door from slamming against...