A mass of 4 kg is suspended from a spring and oscillates up and down at 2 Hz. Determine the stiffness of the spring if the amplitude of the oscillation is 5 mm. Determine the displacement, velocity, and acceleration 0.02 seconds after the mass passes through the mean or rest position in an upward direction.

mo A 100 kg machine has an unbalanced mass of 1 kg, which is rotating at a constant speed of 500 rpm at an offset of 0.2 meters. Calculate the amplitude of the centrifugal force that will be acting on the ground if the machine is directly anchored to the ground. Also calculate the stiffness of the elastic pad that will be placed under the machine such that only 1/10 of this force will be transmitted to the ground. 0-ot m

A force of 3 N stretches a spring by 1 m.(a) Find the spring constant k.(b) Amass of 4 kg is attached to the spring.At t = 0,the mass is pulled down a distance 1 meter fromequilibrium and released with a downward velocityof 0.5 meters/second. Assuming that dampingis negligible, determine an expression for the positionof the mass at time t. Find the circular frequencyof the system and the amplitude, phase,and period of the motion.

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 () 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.