When a 4 kg mass is attached to a spring whose constant is 196 N/m, it comes to rest in the equilibrium position. Starting at  t = 0, a force equal to  f (t)  =  12e−5t cos 7t  is applied to the system. In the absence of damping, (a) find the position of the mass when  t = π. (b) what is the amplitude of vibrations after a very long time?

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 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.

A particle of mass 3.00 kg is attached to a spring with a force constant of 300 N/m. It is oscillating on a frictionless, horizontal surface with an amplitude of 1.00 m. A 9.00-kg object is dropped vertically on top of the 3.00-kg object as it passes through its equilibrium point. The two objects stick together. (a) What is the new amplitude of the vibrating system after the collision? m (b) By what factor has the period of the system changed? (c) By how much does the energy of the system change as a result of the collision? (d) Account for the change in energy.

A 0.110 kg body undergoes simple harmonic motion of amplitude 7.19 cm and period 0.500 s. (a) What is the magnitude of the maximum force acting on it? (b) If the oscillations are produced by a spring, what is the spring constant?

A system with 100g_mass and a spring constant of k=150N/m has a damping constant y=1.1. ASsume the mass was pulled to the right 30 cm at t=0and released. a)Estimate the time at which the amplitude has decayed to ¼ of its initial value. b)Assume the system is connected to a forcing function given by(in Newtons)F(t)=3coswtEstimate the value of the amplitude at resonance.

A 2-kg mass is attached to a spring with stiffness 56 N/m. The damping constant for the system is 8√√7 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that it will attain?

particle with mass 2.57 kg2.57 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.855 m0.855 m and a duration of 129 s129 s for 7272 cycles of oscillation. Find the frequency, ?,f, the speed at the equilibrium position, ?max,vmax, the spring constant, ?,k, the potential energy at an endpoint, ?max,Umax, the potential energy when the particle is located 60.5%60.5% of the amplitude away from the equiliibrium position, ?,U, and the kinetic energy, ?,K, and the speed, ?,v, at the same position.

A 3-kg mass is attached to a spring with stiffness 60 N/m. The damping constant for the system is 12√5 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that it will attain?

A 63.0 kg bungee jumper jumps off a bridge and undergoes damped simple harmonic motion. If the amplitude of oscillation reduces to 0.3679 of the initial amplitude in 0.773 s, what is the damping coefficient?