A linear second order, single degree of freedom system has a mass of 8 x 103 kg and a stiffness of 1000 N /m. Calculate the natural frequency of the system. Determine the damping coefficient necessary to just prevent overshoot in response to a step input.

An 4-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 20 N/m and the damping constant is 2 N-sec/m. At time t = 0, an external force of F(t) = 2 cos (2t + ) is applied to the system. Formulate the initial value problem describing the motion of the mass and determine the amplitude and period of the steady-state solution. Let y(t) to denote the displacement, in meters, of the mass from its equilibrium position. Set up a differential equation that describes this system. (give your answer in terms of y, y', y"). The amplitude of the steady-state solution is m. The period of the steady-state solution is radians. If you don't get this in 3 tries, you can get a hint.

A mass of 2 kg on a spring with k = 6 N/m and a damping constant c= 4 Ns/m. Suppose Fo = v2 N. Using forcing function Fo cos(wt), find the w that causes practical resonance and find the amplitude.

An object weighing 32 lb stretches a spring 2ft in equilibrium. There is also a damping force with c = 8. The spring is raised 2 ft and thrown upwards with a velocity of 4ft/sec. Determine the mass m and the spring constant k, and give the differential equation describing the harmonic motion of this system. Solve the differential equation to find the displacement y.

An object stretches a spring 6 centimeters in equilibrium. Find its displacement for t>0 if it is initially displaced 3 centimeters above equilibrium and given a downward velocity of 6 centimeters/sec. Assume that there’s no damping.

H In a damped oscillator, let m = 250 g, k=85 N/m, and b=0.070 kg/s. In how many periods of oscillation the mechanical energy of the oscillator drop to one-half of its initial value?

A cart of mass m = 1.6 kg placed on a frictionless horizontal surface and connected to a spring with spring constant 6 N/m. The damping force strength is given by b = 255 g/s. The cart is pulled away 16.5 cm and released. k m 'b a. Calculate the time required for the amplitude of the resulting oscillations to fall to 1/7 of its initial value. 24.4 b. How many oscillations are made by the cart in this time? 7.51

The suspension system of a 2100 kg automobile "sags" 7.0 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 45% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming each wheel supports 525 kg. (a) Number (b) Number 73500 Units N/m Units kg/s 4

A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency f = 1.80 Hz. Block B rests on it, and the coefficient of static friction between the two is µ. = 0.640. What maximum amplitude of oscillation can the system have if block B is not to slip? cm Ms P

An object with mass 0.150 kg is acted on by an elastic restoring force with force constant 10.8 N/m. The object is set into oscillation with an initial potential energy of 0.150 J and an initial kinetic energy of 6.00×10−2 J. What is the value of the phase angle ϕ if the initial velocity is positive and the initial displacement is negative?