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- Show that t, e^t, and sin(t) are linearly independent.What is the Jacobi equation?An accelerometer has a damping ratio of 0.4 and a natural frequency of 18, 000 Hz. It is used to sense the relative displacement of a beam to which it is attached. If an impact to the beam imparts a vibration at 4500 Hz, estimate the dynamic error and phase shift in the accelerometer output. Estimate its resonance frequency.
- The cantilever beam shown in Figure 2.1 is subjected to linearly distributed loads. a) Draw all necessary free-body diagrams using the method of sections and find symbolic expressions for the internal shear force (V(x)) and bending moment (M(x)) due to the external forces as functions of x, where x is a horizontal coordinate along the length of the beam, measured from the most left support of the beam. Your expression(s) must allow to obtain internal reactions for 0Make an example of an autonomous ODE, with stable equilibrium at -1 and 3, and an unstable equilibrium at 0What does it mean for the differentiability of a function if only one of the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) holds?
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