An automobile is modeled as a single-degree-of-freedom system vibrating in the vertical direction. It is driven along a road whose elevation varies sinusoidally. The distance from peak to valley (e) is 0.2 m and the distance along the road between the peaks is 35 m. If the natural frequency of the automobile is 2 Hz and the damping ratio of the shock absorbers is 0.15, determine the amplitude of vibration of the automobile at a speed of 60 km/hour. If the speed of the automobile is varied, find the most unfavorable speed for the passengers.

[6] An instrument panel weighing 30 lb is installed in a vehicle on a flexible mount that has an equivalent stiffness k = 400 lb/in and negligible damping. As a result of engine vibration, the vehicle vibrates with a steady-state amplitude of o.25 in at a frequency of 40 Hz. Determine the steady-state amplitude of vibration of the instrument panel.

A 100 kg flow monitoring device is placed on a table in a laboratory. A pad of stiffness 2 x 105 N/m and damping ratio 0.051 is placed between the apparatus and the table. The table is bolted on the laboratory floor. Measurements indicate that the floor has a steady state vibration amplitude of 0.8 mm at a frequency of 50HZ. What is the amplitude of acceleration of the flow monitoring device? Select one: O 2 m/s? O 3 m/s? O 13.65 m/s2 3.9 m/s? TOSHIBA

A weight attached to a spring of stiffness 3.0 lb/in has a viscous damping device. When the weight is displaced and released, the period of vibration is found to be 1.80 seconds and the ratio of consecutive amplitudes is 4.2 to 1.0. Determine the amplitude and phase angle when a force F-2cos(3t) acts on the system.

When an object with a mass of 5 kg is connected to the end of a spring, the spring extends 10 meters and reaches equilibrium. This spring-mass system is placed in an environment with a damping constant of 5 kilograms/second, and the mass is pulled down √ 3 meters from the equilibrium position and released without initial velocity. Find the function that shows the time-dependent change of the position of the given damped spring-mass system. Determine the period and amplitude of the movement. Determine how many seconds it takes for the system to first pass the maximum position (in the positive or negative direction) and the equilibrium position after t = 0. (gravity = 10 meters/second) Then transform the equation of the mass-spring system into a system of equations and draw a sample orbit by creating the vector field of the system and interpret the shape of this orbit.

A damped spring – mass system has a mass of 2 kg, a spring of stiffness 98 N/m and a dashpot with a viscous damping coefficient of 42 Ns/m. If the mass is disturbed by 70 mm and then released from rest, determine the displacement of the mass after 0·12 seconds

Q.4 A damped single degree of freedom mass-spring system is excited at resonance by a harmonic forcing function which has an amplitude of 40 N. The system has mass m of 3 kg, a stiffness coefficient k of 2700 N/m, and a damping coefficient c of 20 N·s/m. If the initial conditions are such that xo = 5 cm, and xo = 0, determine the displacement, velocity, and acceleration of the mass after t = 0.2 s.

A vehicle is modelled as a combined mass-spring-damper system that oscillates in the vertical direction only. The driver of the vehicle travels along a road whose elevation varies sinusoidally as shown in Figure 2. The mass of the vehicle, which includes the driver, is 2500 kg. The stiffness and damping of the shocks are 40 kN/m and 3000 kg/s respectively. i. Determine the amplitude of vibration of the vehicle when it travels at a constant speed of 90 km/hr along the sinusoidal road. y/m 0.6 ►Velocity of vehicle m 0.4 ► Rigid massless tyre 0.2 distance (m) 20 60 80 -0.2 Figure 2