A 1 kg mass is attached to a horizontal spring with stiffness 4 N/m. Initially, the spring is at rest. At time t = 0 an external force, measured in Newtons, F(t) = 3 cos(2t) is applied to the spring. The damping constant is zero. The function y(t) describes the displacement, measured in meters, of the mass from the rest position at time t measured in seconds. Choose all correct statements: a. y" + 4y = 3 cos(2t). O b._y" + 4y = 0. O c. The amplitude of the oscillations of y(t) is 3. Od. The system is at resonance.

A 1 kg mass is attached to a horizontal spring with stiffness 4 N/m. Initially, the spring is at rest. At time t = 0 an external force, measured in Newtons, F(t) = 3 cos(2t) is applied to the spring. The damping constant is zero. The function y(t) describes the displacement, measured in meters, of the mass from the rest position at time t measured in seconds. Choose all correct statements: a. y" + 4y = 3 cos(2t). O b._y" + 4y = 0. O c. The amplitude of the oscillations of y(t) is 3. Od. The system is at resonance.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter3: Oscillations

Section: Chapter Questions

Problem 3.10P: If the amplitude of a damped oscillator decreases to 1/e of its initial value after n periods, show...

See similar textbooks

Similar questions

Show that, if a driven oscillator is only lightly damped and driven near resonance, the Q of the system is approximately Q2(TotalenergyEnergylossduringoneperiod)
If the amplitude of a damped oscillator decreases to 1/e of its initial value after n periods, show that the frequency of the oscillator must be approximately [1 − (8π2n2)−1] times the frequency of the corresponding undamped oscillator.
A mass of 1 slug is attached to a spring whose constant is 25 > 4lb > ft. Initially the mass is released 1 ft above the equilibrium positionwith a downward velocity of 3 ft > sec, and the subsequentmotion takes place in a medium that oers a damping force numericallyequal to 3 times the instantaneous velocity. An externalforce ƒ(t) is driving the system, but assume that initially ƒ(t) K 0.
A simple pendulum is constructed by placing a small ball of mass 0.2g at the end of string of length 0.9m. Supposing the string to be massless, what is the period (in seconds) of oscillation for small angular displacements?
A spring with constant k = 5 N/m hanging from the ceiling is placed at its lower end with an object of 1 N, which causes it to remain in equilibrium. The weight is then pulled 0.5 m above the equilibrium position.and is released with no initial velocity. There is no damping force acting on the system. SI x(t) represents the displacement of the weight, in meters, from the equilibrium point and taking upwards as thepositive direction, an equation that describes the position of the weight as a function of time t (in seconds) is:If necessary, use the gravity constant g as g = 9.8 m/s2 Possible answer in the images.
Given that a damped oscillation of a mass M = 250 g attached to a spring with a force constant K = 85 N/m and damping constant b = 75g/s. A) calculate the period of oscillation. B) find the time taken for the amplitude of the damped oscillation to drop to half of its initial value.
A block of mass m = 249 grams oscillates to the left and right with negligible friction on the end of an ideal spring with a spring constant of 117 N/m. At the time t = O, the block is a distance 0.145 m to the right of the equilibrium position and it is moving to the right with a speed of 3.1 ms. What is the velocity of the block (in units of meters per second) at the time when t = 0.129 seconds? The sign (positive or negative) of your answer is important. For the purposes of this question, velocity pointing to the right is positive and a velocity to the left is negative.
After a mass m is attached to a spring, the spring is stretched s units and hangs at rest at the equilibrium position as shown in Figure 1.3.17(b). Then the spring/mass system is set in motion, let x(t) denote the directed distance from the equilibrium point to the mass. As shown in Figure 1.3.17(c), assume that the downward direction is positive and that the motion is on a vertical straight line through the center of gravity of the mass and that the only forces acting on the system are the weight of the mass and the restoring force of the stretched spring. Use Hooke's law: the restoring force of a spring is proportional to its total elongation. Determine a differential equation of the displacement x(t) at time t>0. please answer as soon as possible :)
Consider a simple harmonic oscillator consisting of a one kilogram mass m' on a spring with spring/forceconstant k and length L'. If the mass of the spring ms is 9% of the attached mass, and k = 66 N/m,and if we determined the attached body is displaced 3 cm and given a downward velocity of 0.4 m/s -calculate,→ the frequency ω of the motion, ,→ and the amplitude A of the motion
If we attach two blocks that have masses m1 and m2 to either end of a spring that has a force constant k and set them into oscillation by releasing them from rest with the spring stretched, show that the oscillation frequency is given by v = (k/m)^1/2, where m = m1m2 /(m1 + m2) is the reduced mass of the system.
The maximum velocity attained by the mass of a simple harmonic oscillator is 10 cm/s, and the period of oscillation is 2 s. If the mass is released with an initial displacement of 2 cm, find (a) the amplitude, (b) the initial velocity, (c) the maximum acceleration, and (d) the phase angle.
In the above question let us consider the position of mass when the spring is relaxed as x = 0, and the left to right direction as the positive direction of the x-axis.Provide x as a function of time t for the oscillating mass, if at the moment we start the stopwatch (t = 0), the mass is:( i ) at the mean position,( ii ) at the maximum stretched position, and( iii ) at the maximum compressed position.