Problem 1 (Harmonic Oscillators) A mass-damper-spring system is a simple harmonic oscillator whose dynamics is governed...
A simple harmonic oscillator is made up of a mass-spring system, with mass of 2.33 kg and a spring constant k = 170 N/m. At time t=1.51 s, the position and velocity of the block are x = 0.11 m and v = 3.164 m/s. What is the velocity of the oscillation at t=0? Be sure to include the minus sign for negative velocity.
A simple harmonic oscillator is made up of a mass-spring system, with mass of 2.82 kg and a spring constant k = 124 N/m. At time t=1.18 s, the position and velocity of the block are x = 0.127 m and v = 3.618 m/s. What is the velocity of the oscillation at t=0? Be sure to include the minus sign for negative velocity. Your answer should be in m/s, but enter only the numerical part in the box.
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mi+ci +kx- Asin(ot) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor un-damped natural frequency on a. and the
A second order mechanical system of a...
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Consider an ideal mass-spring-damper system similar to Figure 3.2. Find the damping coefficient of the system if a mass of 380 g is used in combination with a spring with stiffness k = 17 N/m and a period of 0.945 s. If the system is released from rest 5 cm from it's equilibrium point at to = 0 s, find the trajectory of the position of the mass-spring-damper from it's release until t 3s Figure 3.2: Mass-spring-damper...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
Problem: A simple harmonic oscillator has a block of mass 1.7 kg attached to a spring (k = 260 N/m). When t = 2 s, the block's position and velocity are x = 0.135 m and v = 4.06 m/s. (a) What is the amplitude? What were the (b) position and (c) velocity of the block at zero seconds? part a = .3549 part b = .2529 m Please solve for part c.
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
5) A damped simple harmonic oscillator consists of a.40 kg mass oscillating vertically on a spring with k- 15 N/m with a damping coefficient of .20 kg/s. The spring is initially stretched 17 cm downwards and the mass is released from rest. a) What is the angular frequency of the mass? b) What is the position of the mass at t-3 seconds? c) Sketch a position vs time graph for the mass, showing at least 5 full cycles of oscillation....
For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - 5 sin 2t (N) f2(t)-t (N) l. Formulate an IVP for vibration analysis in terms of xi (t) and x2(t) in a matrix form. Assume that the 2. Solve an eigenvalue problem to find the natural frequencies and modeshape vectors of the system 3. What is the modal matrix of the system? Verify the orthogonal properties of the modal matrix, Ф, with system...
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following second order linear ODE: dx,2 dt n dt2 (0) C dt where is the damping ratio an wn is the natural frequency, both related to k, b, and m (the spring constant, damping coefficient, and mass, respectively) (a) Use the forward difference approximations of (b) Using Δt andd to obtain a finite difference formula for x(t+ 2Δ) (like we did in class for the...