A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 9 ft/s. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = 9te-2√2t Find the time t = 0.3535 which the mass attains its extreme displacement from the equilibrium position. x What is the position of the mass at this instant? The extreme displacement is x = 2.34 x feet.

A mass-spring motion is governed by the ordinary differential equation d²x dx +b + k(t)x= F(t), dt² dt m where m is the mass, b is the damping constant, k is the spring constant, and F(t) is the external force. We consider the initial conditions x(0) = 1 and x/(0) = 0. Assume the following numerical values for this part of the project: m = 1, k = 1/5, b= 1/5, and F(t) = cos yt. 1 (a) Read section 4.10. Explain what is the resonance frequency, and then compute the resonance frequency for this mass-spring system. (b) The ODE45-solver can be used to obtain the solution curves in MATLAB. Use the script Project2_Q2.m to plot the solutions and estimate the amplitude A of the steady response for y = 0.2, 0.42, 0.6, and 0.8. (c) The script also provide you with the graph of A versus y. For what frequency 7 is the amplitude the greatest? Is it equal to that you obtained in (a)?

A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 3 ft/s. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = Find the time at which the mass attains its extreme displacement from the equilibrium position. t= X x What is the position of the mass at this instant? The extreme displacement is x = 0.39 X feet.

A tuning fork is struck and oscillates in damped harmonic motion. The amplitude of the motion is measured, and 4 s later it is found that the amplitude has dropped to  1 3  of this value. Find the damping constant c for this tuning fork. (Round your answer to two decimal places.)

A block with mass M rests on a frictionless surface and is connected to a horizontal spring of force constant k.  The other end of the spring is attached to a wall.  A second block with mass m rests on top of the first block.  The coefficient of static friction between the blocks is μs.  Find the maximum amplitude of oscillation such that the top block will not slip on the bottom block. What the period of oscillation for the situations where the little mass (m) remains on the big mass (M) and when it doesn't.

A driving force of the form F (t) = (0.260 N) sin (27 ft) acts on a weakly damped spring oscillator with mass 5.63 kg, spring constant 373 N/m, and damping constant 0.163 kg/s. What frequency fo of the driving force will maximize the response of the oscillator? fo = Hz Find the amplitude A, of the oscillator's steady-state motion when the driving force has this frequency. Ao = about us privacy policy terms of use contact us help careers

The period of motion of an object-spring system is T = 0.642 s when an object of mass m= 266 g is attached to the spring. (a) Find the frequency of motion in hertz. (b) Find the force constant of the spring. (c) If the total energy of the oscillating motion is 0.176 J, find the amplitude of the oscillations. please show every step so I can learn how to do it. Thank you!

A mass of 16 kilograms is suspended from a spring with spring constant 7 Kg/sec^2. The damping constant is 2 Kg/sec and the spring is subject to an external force F(t)= 3cos(9t) Newtons. The motion of the mass eventually settles down to a periodic oscillation. What is the period (in sec) of this periodic oscillation? 2 9.

Given a horizontal spring, an object with a mass of 5 kg is pulled to the right 15 cm to the right. (Observation was made that during 8 seconds 12 oscialtions occured druing the trial).  Find the postion and velocity after 1-second.  Use equation: x(t) = Acos(wt +phi) where A is max amplitude  w is angular frequency  t is time  and phi is phase

A-kg mass is attached to a spring with stiffness 25 N/m. The damping constant for the system is 4 N-sec/m. If the 15 55 mass is moved 8 m to the left of equilibrium and given an initial rightward velocity of m/sec, determine the equation of motion of the mass and give its damping factor, quasiperiod, and quasifrequency. What is the equation of motion? y(t) = (Type an exact answer, using radicals as needed.) ***