4.3.3. A square membrane with sides of length L, uniform surface density ps, and uniform tension T is fixed on three sides and free on the other. (a) Find the frequency of the fundamental mode. (b) Write a general expression for the natural frequencies and one for the normal modes. (c) Sketch the nodal patterns for the three normal modes with the lowest natural frequencies.

Find the natural frequency (in Hertz) of the system illustrated in the following figure. K1=731 N/m,  K2=496 N/m,  K3=775 N/m M=0.2 kg, and L=2 m.

QUESTION 3 A machine tool, having a mass of m = 1000 kg and a mass of inertia of Jo = 300 kg.m², is supported on elastic supports, as shown in Figure Q2. If the stiffnesses of the supports are given by kl = 3000 N/mm and k2 = 2000 N/ mm, and the supports are located at 11 = 0,5 m and 12 = 0,8 m, determine the natural frequencies and mode shapes of the machine tool. Develop the state-space model. Use numerical integration to compute and plot the time response of the system (newtons) subject to your own initial conditions. m, k Figure Q3

1. A thin disk attached to the end of an elastic beam has three uncoupled modes of vibration. The longitudinal motion, transverse motion and the torsional oscillations are all kinematically independent. Calculate the following for the system shown. a. Longitudinal stiffness b. Transverse stiffness c. Torsional stiffness mumm 65 cm r= 10 mm E-200 x 10° N/m² G=80 x 10º N/m²

A transverse traveling wave on a taut wire has an amplitude of 0.200 mm and a frequency of 500 Hz. It travels with a speed of 196 m/s. (a) Write an equation in SI units of the form y=A sin (kx - vt) for this wave.(b) The mass per unit length of this wire is 4.10 g/m. find the tension in the wire.

I need the answer as soon as possible

Vibration

H6.

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