Suppose that a car is 900 kg and has a suspension system that has a force constant k = 6.53×104 N/m . The car hits a bump and bounces with an amplitude of 0.100 m. What is its maximum vertical velocity if you assume no damping occurs?

A damped harmonic oscillator consists of a block (m = 2.00 kg), a spring (k = 10.0 N/m), and a damping force (F=-bv). Initially, it oscillates with an amplitude of 25.0 cm; because of the damping, the amplitude falls to three-fourths of this initial value at the completion of four oscillations. (a) What is the value of b? (b) How much energy has been “lost” during these four oscillations?

PROBLEM2: The system shown in Figure 2 has a natural frequency of 5 Hz for the following data: m = 10 kg, Jo = 5 kg - m², r₁ = 10 cm, r₂ = 25 cm. When the system is disturbed by giving it an initial displacement, the amplitude of free vibration is reduced by 80 percent in 10 cycles. Determine the values of k and c. T2 m x(1) Figure 2 0000 k Pulley, mass moment of inertia Jo

Industrial processes often require the damping of vibrations. Consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of ?=59800 N/m. This workbench is used when creating products that involve highly unstable chemicals. According to specifications, the acceleration of the manufacturing equipment must be held to less than 24.0 m/s2 for the manufacturing process to proceed safely. The amplitudes of vibrations are expected to remain under 0.532 mm throughout. Given that the workbench and maufacturing equipment have a combined mass of ?=6.05 kg, find the maximum acceleration ?max expected of the equipment and workbench. Ignore the mass of the springs. ?max= m/s2 Does the workbench meet the specifications for acceleration? yes no An engineer decides to damp the oscillations by applying one shock absorber to each spring. These shock absorbers apply a…