Please help me Thanks in advance Mechanical vibration questi

Please help me! Thanks in advance. Mechanical vibration question.

The crash behavior of a vehicle and bumper system may be modeled as a free vibration of a one-degree-of-freedom dynamic with viscous damping Zeta has a general form of a second-order governing differential equation of motion. Therefore, the state of response equation X(t)can be expressed as, X_YS(t) = e^-zetaomega_nt/2Squarerootzeta^2 - 1{[X_u/omega_u + X_u(zeta + Squarerootzeta^2 - 1)]e^(omega_nSquarerootzeta^2 - 1)t + [-X_u/omega_u + X_u (-zeta + Squarerootzeta^2 - 1)]e^-[omega_nSquarerootzeta^2 - 1)t} for an overdamped (damping factor zeta > 1) free vibration at an initial condition of X(0) = X_0 and X(0) = X_0. Assuming the equivalent system is modeled with a discrete mass m = 25 times 10^3 kg has a linear spring (k = 3 times 10^5 N/m) in parallel with a viscous damper (c = 1.73 times 10^5 kg/s). Determine the answers from part (a) to (e) for the above described model:- Derive the specific transient response equation of vibration of the system at initial boundary condition X(0) = 0 and X(0) = 2.7 m/s.

Solution

Biomedical Imaging Question: Using the figure above, calculate the X-ray intensity, as a function of the incident intensity I0, that reaches the detector for each of the three X-ray beams. The dark-shaded area represents bone, and the light-shaded area represents tissue. The linear attenuation coefficients at the effective X-ray energy of 68 keV are 10cm-1 for bone and tissue, respectively.