The Fourier series for a periodical square wave is O sin (wt) + = sin(3wt) + ½ sin(5wt) + O sin (wt) + = sin(2wt) +½ sin(4wt) + ² F sin (wt) + sin(3wt) + 1 1 sin (wt) += cos(3wt) + 2 sin(5wt) + A sin(5wt) +

P

find the Fourier series represen- tation of the given function over the indicated fundamental interval and use a computer to plot the indicated partial sum Sn(x) over the fundamental interval. f(x) = { 0, sinx, 0≤x≤л. Plot Sε(x).

Mechanical Vibration Question is image

Example m₁ = m₂ = m3 = m. Solution: The dynamical matrix is given by [D] = [k]¹[m] = [a][m] (E.1) a11 a12 ain 921 922 [k]¯¹ = [a] = anl an2 Find the natural frequencies and mode shapes of the system shown in the Fig. for k, = k₂ = k3 = k and F F(0) FX(t) 00 me a2n Ann JEET kr m₂ k;

Phase (deg) Magnitude (dB) 20 20 40 180 135 90 45 10' 0 ġ(t) 하 R www Mechanical Deformation Piezo Charge Amplifer 10 10 Frequency (rad's) v(t) Figure 2: Frequency response function of a microphone Figure 3: A simple model for piezoelectric sensor 3. Figure 3 is a simple circuit modeling a piezoelectric sensor. Mechanical deformation of the sensor induces charge q(t), which is first modeled as a current source. The capacitance C models the piezoelectric material, and the resistance R represents impedance of a charge amplifier with output voltage v(t). Usually, C is fixed for a sensor, but R is adjustable from the amplifier. The frequency response function from q(t) to v(t) is Answer the following questions. G(w)= = jRw 1+jRCw (6) (a) Consider the case when C = 1 Farad and R = 0.5 Ohm. (The numbers are chosen to ease calculations. In practical applications, C is much smaller and R is much bigger.) If the input deformation induces electric charge = q(t) cost+2 sin 3t (7) predict the…

The differential equations of motion of a 2-D system are determined as: (see image) Find the system’s natural frequencies and mode shapes.

The problem is in the photo

The problem is in the photo

for the moments is there not 3 ?  please refer to the image attached. have i gone wrong somewhere?