A mass of 0.2kg attached to a spring with aspring constant of 5N/m performs simple harmonic motion.The time-dependent graph of the position of the mass withan initial velocity of 0.5m/s is shown below. If the positionof the mass is expressed as x(t)=Acos(Bt+C), what is thevalue of the constants A, B, and C that define this motion?x(t) (cm)2t(s)

Answered: Image /qna-images/answer/59ccc790-e032-494e-b02d-6de3125f59a1.jpg

A mass of 0.2kg attached to a spring with a unt of 5N/m performs simple harmonic motion. pendent graph of the position of the mass with ocity of 0.5m/s is shown below. If the position is expressed as x(t)=Acos(Bt+C), what is the constants A, B, and C that define this motion?

A mass of 0.2kg attached to a spring with a unt of 5N/m performs simple harmonic motion. pendent graph of the position of the mass with ocity of 0.5m/s is shown below. If the position is expressed as x(t)=Acos(Bt+C), what is the constants A, B, and C that define this motion?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x = 0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the mass of the object, and k is the spring constant. A mass of 3 kilograms stretches the spring 0.2 meters. dt² Use this information to find the spring constant. (Use g = 9.8 meters/second²) m k = + kx The previous mass is detached from the spring and a mass of 17 kilograms is attached. This mass is displaced 0.45 meters below equilibrium and then launched with an initial velocity of 2 meters/second. Write the equation of motion in the form x(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants in your equation. x(t) = Rewrite the equation of motion in the form ä(t) = A sin(wt + ), where 0 ≤ ¢ < 2π. Do not leave unknown constants in your equation. x(t) =
4. Consider a mass of 500 g placed at the end of a spring with stiffness constant 100 N/m and hanging at rest. The mass is displaced downward by 1.0 cm and released from rest. When the motion sets in, a time-varying force F(t) = cos³ 2t is applied to the spring-mass system. Solve the nonhomogeneous 2nd order differential equation representing the motion. That is, solve for x(t). [Note: Take the downward direction as the negative x-axis.]
This problem is an example of over-damped harmonic motion. A mass m = 3 kg is attached to both a spring with spring constant k = 36 N/m and a dash-pot with damping constant c = 21 N. s/m. The ball is started in motion with initial position = -6 m and initial velocity vo = 3 m/s. Determine the position function (t) in meters. x(t) = Graph the function z(t).
6. A 1kg mass is attached to a spring (with spring constant k = 4 N/m), and the spring itself is attached to the ceiling. If you pull the mass down to stretch the spring past its equilibrium position, when you release the mass and observe its (vertical) position, it's said to undergo simple harmonic motion. AT REST MASS PULLED DOWN wwww Under certain initial conditions, the mass's vertical position (in metres) relative to its equilibrium position at time t, y(t), can be modelled by the equation y(t) = cos(2t) – sin(2t), (Note that y measures how much the spring has been stretched, so y = 1 indicates the mass is Im below its equilibrium position, whereas y = -1 indicates it is 1m above its equilibrium position.) (a) Find expressions for the mass's (vertical) velocity v(t) (relative to its equilibrium position) and the mass's (vertical) acceleration a(t) (relative to its equilibrium position). (b) Is the mass moving toward the ceiling or toward the floor at t= T? Justify your answer with…
A 0.1kg object oscillator as a simle harmonic motion along the x _axis with a frequency f=3.18 hz at a position x1,the object has a kinetic energy 0.7j and a potential energy 0.3j,the amplitude of oscillation A is:
5. A mass on a spring is shown below. Let y(t) be the displacement of the spring as a function of time t. Position A is the equilibrium position corresponding to y = 0. As was done in class, we are taking the positive direction to be downward. The graph of the solution to an initial value problem for this spring is shown. Answer the following questions about this system. A m B A: y=0 C (a) The spring's starting position (at t = 0) could be at i. Position A (Equilibrium) ii. Position B (Above Equilibrium) iii. Position C (Below Equilibrium) iv. Not enough information to tell (b) The spring's starting velocity (at t = 0) is i. positive ii. zero iii. negative iv. Not enough information to tell (c) Immediately after being set in motion at t = 0) the spring
The complete slide- back and forth motion of a single reciprocating compressor piston completes in a 2-sec period. The volume displacement of the piston though the piston cylinder is 8,902.63 in3. The stiffness of crank is said to be equal to 65.5N/m and the mass of the said piston is at 10kgs. 1) The natural frequency 2) Force exerted by the piston 3) Draw the piston assembly along with its motion and position analysis
1 An object of mass 125 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy force of times the weight of the object is pushing the object up (weight = mg). If we assume that water 40 resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10 N-sec/m, find the equation of motion of the object. After how many seconds will the velocity of the object be 90 m/sec? Assume that the acceleration due to gravity is 9.81 m/ sec2. Find the equation of motion of the object. X(t) = %3D
Harmonic oscillators. One of the simplest yet most important second-order, linear, constant- coefficient differential equations is the equation for a harmonic oscilator. This equation models the motion of a mass attached to a spring. The spring is attached to a vertical wall and the mass is allowed to slide along a horizontal track. We let z denote the displacement of the mass from its natural resting place (with x > 0 if the spring is stretched and x 0 is the damping constant, and k> 0 is the spring constant. Newton's law states that the force acting on the oscillator is equal to mass times acceleration. Therefore the differential equation for the damped harmonic oscillator is mx" + bx' + kr = 0. (1) k Lui Assume the mass m = 1. (a) Transform Equation (1) into a system of first-order equations. (b) For which values of k, b does this system have complex eigenvalues? Repeated eigenvalues? Real and distinct eigenvalues? (c) Find the general solution of this system in each case. (d)…
The figure that is attached illustrates a system in which a force F is applied to a mass m2 that is connected to another mass m1 via a spring and a damper, and mass m1 is connected to a wall via a damper. The equations of motion that govern the time evolution of the mass displacements, y1(t)and y2(t), are given below. A) Define 4 state variables of the system (xi, i = 1,…,4) as phase variables, and define the control input u. Convert the two equations of motion above into four 1st-order ODEs that are functions of the state variables and the control input.(b) Write the four 1st -order ODEs from part (a) in state-space form,x = Ax+Bu.
A spring with mass 1 kg is attached to one side of a spring with spring constant k = 12 kg/sec2. The other end of the spring is connected to the side of a steel beam so that the spring may oscillate in the horizontal direction. Suppose that friction is proportional to velocity with constant of proportionality f = 7 kg/sec. Write a differential equation for y(t), the position of the mass at time t, with the initial conditions y(0) = 0 and y(0) =1 m/sec. Solve your resulting IVP.
A spring has an unstretched length of 12 cm. When an 80 g ball is hung from it, the length increases by 4.0 cm. Then the ball is pulled down another 4.0 cm and released.a. What is the spring constant of the spring?b. What is the period of the oscillation?c. Draw a position-versus-time graph showing the motion of the ball for three cycles of the oscillation. Let the equilibrium position of the ball be y = 0. Be sure to include appropriate units on the axes so that the period and the amplitude of the motion can be determined from your graph.