Question 1: A particle of mass m is attached to a horizontal spring with constant k and submerged in a fluid with damping coefficient b. The system is influenced by an external periodic force F.sin(wt+0) i. 1- Write the differential equation of the motion 2- If m=2 kg, k = 4 N/m, and b = 3 N.s.m', deduce: a) The natural frequency w b) The resonance frequency w

Question 1: A particle of mass m is attached to a horizontal spring with constant k and submerged in a fluid with damping coefficient b. The system is influenced by an external periodic force F.sin(wt+0) i. 1- Write the differential equation of the motion 2- If m=2 kg, k = 4 N/m, and b = 3 N.s.m', deduce: a) The natural frequency w b) The resonance frequency w

Name: Question 1:A particle of mass m is attached to a horizontal spring wi
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: Question 1:A particle of mass m is attached to a horizontal spring with constant k and submerged in a fluidwith damping coefficient b. The system is influenced by an external periodic forceF.sin(wt+0) i.1- Write the differential equation of the moti

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A mass m = 3.3 kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A = 4.5 cm and a frequency f = 1.5 Hz. a. Write an equation for the spring constant k. b. Calculate the spring constant k, in Newtons per meter. c. Write an equation for the total mechanical energy, E, of the motion. Your expression should be in terms of the variables in the original problem statement. d. Calculate the total mechanical energy E, in joules.
2.3. The solution for damped simple harmonic motion is given by -rt/2m(C, eiw't + Cze-iw't) X = e If x = A coso at t= 0, find the values of C, and C2 to show that i = -w'Asin o at t = 0 only if r/m is very small or o = T/2. 2.4. A capacitance C with a charge qo at t = 0 discharges through a resistance R. Use the voltage equation q/C + IR = 0 to find charge and the relaxation time of this process.
Two GFRP composite coupons, 25 mm wide with ply thicknesses of 0.125 mm, have the lay-up (03/902)s and (902/03)s. The ply elastic constants are E, = 40 GPa, Ez = 10 GPa, v12 = 0.3 and G12 = 4 GPa. i) Sketch the LPT layer system for the (03/902)s labelling the Zk distances. ii) Calculate the in-plane elastic properties for each coupon.
K A loudspeaker diaphragm is oscillating in simple harmonic motion described by the equation d = a cos (ot) with a frequency of 648 hertz (cycles per second) and a maximum displacement of 1.10 millimeter. Find @ and then determine the equation that describes the movement of the diaphragm. ….
3. The velocity at any time t of a simple harmonic oscillator is given by: v(t)= -5.884sin(26.203t), where v is in m/s andt in sec. Where is the mass (position in meters) at the time 185.229 seconds? Hint: either set your calculator on radian or convert the phase into degrees.
8. A weight of 0.5kg stretches a spring by 0.49m. The spring-mass system is submerged in delicious melted butter with a damping coefficient of y=4. The spring is then lowered by an additional 1.0m and released with velocity 0. There is no external force. Find the function which gives the location of the weight at time t. Note: I have designed this to work out nicely. If it's not working out nicely then you probably got some butter in your calculations.
solv
BCQj19YQPvX8JEsbA/formRespor 0.25 sec O 2 sec 1 sec The equation of motion of a particle in simple harmonic motion is given by: x(t) = 0.1cos(wt), where x is in meters and t is in seconds. At x = 0, the particle's velocity is v = -1.256 m/s. The period of oscillation, T, equals: O1.5 sec 3 sec 0.25 sec
3
Answers : 0.1026 in and 5.16 in/sshow complete solution and answer
s An atom in a molecule oscillates about its equilibrium position with a frequencyof 2.00 * 1014Hz and a maximum displacement of 3.50 nm.(a) Write an expression giving x as a function of time for this atom,assuming that x = A at t = 0. (b) If, instead, we assume that x = 0at t = 0, would your expression for position versus time use a sinefunction or a cosine function? Explain.
A light balloon filled with helium of density 0.179 kg/m³ is tied to a light string of length L = 5.45 m. The string is tied to the ground, forming an "inverted" simple pendulum (shown in (a) of following figure). Air a 100->> L He Air L He i Determine the period of the motion (in s). Take the density of air to be 1.18 kg/m³. (Hint: Use an analogy with the simple pendulum. Assume the air applies a buoyant force on the balloon but does not otherwise affect its motion.)