A spring/mass/dashpot system has mass 9 kg, damping constant 288 kg/sec and spring constant 3249 kg/sec/sec. Express the ODE for the system in the form I"+2px'+wr=0 Identify the natural (undamped) frequency of the spring: (square Hz) = ولا Identify the parameter p: p= (Hz)
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- A 1.30 kg mass oscillates according to the equation x = meters and t is in seconds. Determine the amplitude. 0.500 cos 8.30t, where x is in HA A = Value Units Submit Request Answer Part B Determine the frequency. µA ? f = Value Units Submit Request Answer Part C Determine the total energy. HÁ ? Etotal Value Units %3DA-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.) ***What frequency is depicted in the following equation of an oscillator? Assume that the units work out and the amplitude is in millimeters and the time tt is in seconds. x(t)=−2.2sin(40t−π3)x(t)=−2.2sin(40t−π3) a. 6Hz6Hz b. 20πHz20πHz c. 16Hz16Hz d. 180πHz180πHz e. π20Hzπ20Hz f. 80πHz80πHz
- s= If a particle undergoes SHM with amplitude 0.19 m, what is the total distance it travels in one period? Express your answer using two significant figures. ΜΕ ΑΣΦ ? BA mass 5-kilogram attached to end of a spring that is stretched 20 cm by a force of 9N. It is set in motion with initial position x(0)=0 and velocity v(0)= -10 m/s. Find the amplitude and the frequency of the resulting motion. Enter exact answers and use pi for "Amplitude = "Frequency = m" HZ"Energy (J) 20 PE 15 10- 10 5 12 16 20 24 24 28 25 . Suppose the damping constant b of an oscillator increases. a. Is the medium more resistive or less resistive? b. Do the oscillations damp out more quickly or less quickly? c. Is the time constant 7 increased or decreased? TE x (cm)
- A box of a certain mass is attached to a spring of spring constant 7.0 N/m and experience simple harmonic motion with an amplitude of 0.2 m. When the position of a box is at 0.4 A its speed is measured to be + 0.25 m/s. (Hint: x(t) = Asinwt). Calculate the angular frequency (w). А. 3.46 Hz B. 2.72 Hz C. 4.22 Hz D. 1.36 HzThe amplitude of a lightly damped oscillator decreases by 1.2% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle? Number Enter your answer in accordance to the question statement Units Choose the answer from the menu in accordance to the question statement g (gravity)kg/satomskm/h^2rev/minmegatonsft·lbhpdollarshits/satmL/minpercentcm^-3 or /cm^3s/hsmu/ylines/mmcentsuphotons/sphotons/s·m^2ktonm^-3 or 1/m^3kg/minN-s/mN/storr or mm Hgmg/sμmAn 9-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 20 N/m and the damping constant is 4 N-sec/m. At time t= 0, an external force of 8 sin 2t cos 2t is applied to the system. Determine the amplitude and frequency of the steady-state solution. The amplitude is (Type an integer or a decimal. Round to four decimal places as needed.)