Question

 Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics:

 Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f₀ = 5 N; forcing frequency, ω_t = 30 rad/s.

 (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped.

 (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine the response and state the condition i.e. underdamped, critically damped, or overdamped.

 (c) Based on your results in (a), obtain the steady-state response if the forcing frequency is reduced by 68 %. Discuss the outcome in terms of the response and its relation to natural frequency, w., and the variation in forcing frequency, ω_f. What is the phenomenon in vibration when this happen?

 (d) Based on your results in (c), how can the effect of vibration be reduced?

 By referring to Figure Q2, a vehicle is modeled as a single-degree-of-freedom system vibrating in the vertical direction. It is driven along a road whose profile varies sinusoidally. The distance from peak to trough is 0.20 m and distance along the road between the peaks in 37 m. If the natural frequency of the vehicle is 2.10 Hz and damping ratio of shock

 absorbed is 0.18:

 (a) Determine the amplitude of vibration of the vehicle at a speed of 55 km/hr.

 (b) If the speed of vehicle is varied, find out the most unfavorable speed for the passengers.

 Figure Q1 shows displacement response of an underdamped single degree-of-freedom

 (SDOF) system. Given, mass, m = 250 kg, and the suspension stiffness, k = 18000 N/m.

 (a) Estimate the damping of the system.

 (b) If the initial displacement of the system is 0.05 m, obtain the equation of motion of

 the system.

 (c) From the information in (b), draw a SIMULINK block diagram of the SDOF system. Name all the blocks used for the above system based on the parameters and the given constants, and those obtained from (a) & (b).

Answer 1