A 1- D.o. F. system is given as shown. Find the equation of motion of the system in terms of the given parameters (c,k,m). For m = 4 kg, k = 3 kN/m and c = 1000 N. s/ m, determine the natural frequency and the damping ratio of the system. 2c 2k 5m %3D 3k k
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- Given DFQ select statememts that are not true7a You are on a fishing trip, not catching anything, and bored - time for physics! You drop your 50g weight to the bottom of the lake under constant tension from the string of magnitude 0.1N. The damping constant for your falling weight is 2.5kg/s. What is the terminal velocity of the weight? Give your answer in m/s and assume the positive direction is upwards b If it takes 500s for the weight to reach the bottom of the lake, how deep is the lake? Give your answer in m.A body of mass __ = 1.10 kg lies quietly on a smooth horizontal plane resting on an ideal spring arranged along the horizontal direction of elestic constant __= 7.00 N/m compressed by __ = 1.40 m with respect to the resting length. At t=0 the spring is left free to expand and the body is accelerated. Determine 1. The module of the speed at which the body leaves the spring 2.The instant of time when it leaves the spring
- A linear second order, single degree of freedom system has a mass of 8 x 103 kg and a stiffness of 1000 N /m. Calculate the natural frequency of the system. Determine the damping coefficient necessary to just prevent overshoot in response to a step input.An automobile suspension system is critically damped, and its period of free oscillation with no damping is 1 s. If the system is initially displaced by an amount and released with zero initial velocity (at t = 0; x(0) =x, and v(0) = 0) %3D a- Determine the value of the angular frequency of free oscillation with no damping. (wo = ??) b- Deduce the value of friction factor (g =??) c- Write the expression of position as a function of time of the system, if the system is critically damped. (x(1) = ??) d- Deduce the expression of the velocity of the system. (v(t) = ??)A 6-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 30 N/m and the damping constant is 3 N-sec/m. At time t=0, an external force of 2 sin 3t cos 3t N is applied to the system. Determine the amplitude and frequency of the steady-state solution. **..*. Using g= 9.8 m/sec", the equilibrium displacement of the mass is (Type an integer or a decimal.)
- A 260 g air-track glider is attached to a spring with spring constant 5.90 N/m. The damping constant due to air resistance is 1.80×10-2 kg/s. The glider is pulled out 34.0 cm from equilibrium and released. Part A -1 How many oscillations will it make during the time in which the amplitude decays to e ΠΙ ΑΣΦ V Submit Provide Feedback Request Answer ? Review of its initial value?O Macmillan Learning A small bolt with a mass of 27.0 g sits on top of a piston. The piston is undergoing simple harmonic motion in the vertical direction with a frequency of 1.45 Hz. Use g = 9.81 m/s² for the acceleration due to gravity. What is the maximum amplitude Amax with which the piston can oscillate without the bolt losing contact with the piston's surface? Amax = mO9
- A2.51 kg mass is attached toa spring. In the absence of damping, its maximum speed is 1.64 m when its amplitude is 12.5 cm It is then immersed in a damping fluid. At what angular frequency should it be driven so its speed is a maximum? rad/s Please give me correct and exact ans if your answer is wrong I surely gives u downvote so if u don't know how to solve please skip correct answer gives u likesAs a function of time, the position of the mass in a damped oscillator is given by the following equation: x=Ae-Btcosωt Which of the following is the velocity of the mass as a function of time and if possible tell me why?16.A. -Ae-Bt(ωcosωt+Bsinωt) B. -Ae-Bt(Bcosωt-ωsinωt) C. -Ae-Bt(Bcosωt+ωsinωt) D. ABe-Bt(sinωt+cosωt) E. None of the aboveConsider an ideal spring with spring constant k = 20 N/m. The spring is attached to an object of mass m = 2.0 kg that lies on a horizontal frictionless surface. The spring-mass system is compressed a distance xo = 50 cm from equilibrium and then released with an initial speed vo= 0 m/s toward the equilibrium position. x=0 equilibrium initial state a. What is the period of oscillation for this system? b. Starting at t = 0, how long will it take for the object to first return to the equilibrium position?