Determine the oscillation amplitude and frequency of the mass in the figure below fort₁ ≤ t ≤ t₂. Assume that the system is vibrating in a steady-state condition during thistime period.What is the frequency of vibration from time t₂ on?F = F₁ sin wtk = 50 N/m0.5 kgc=1 N-s/mF(t) ky(t)↓↓MF, newtonsFoANᏁᏁᏁᏁᏁᏁᏁᏁᏁ[y(1)dy(t)dt8 10-1₂, whenexcitationstops12 141, seconds

Given: Mass→m=0.5 Kg The spring constant→k=50 N/m Damping coefficient→C=1 N.s/m From the figure, the…

Answered: Determine the oscillation amplitude and…

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

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1) For the mass-damper system at right, the model in terms of velocity is mv + cv = f. The time constant of this first order system is t = m/c. For this system, a larger value of the damping constant c causes the time constant to decrease - which is counterintuitive. It seems that a small amount of damping should correspond to a system with a fast response. How can you reconcile this? m CA
General Solution for small oscillations of a simple pendulum with length 5.0 m and mass of 2.0 kg and spring constant of 8 N/m is given as: x = Ccos(0 – 4) VK/m Where w = And 0 = wt Find the numerical values of the a) amplitude of the spring; b) period of the of the spring; c) frequency of the spring.
Consider a spring-mass system with mass equal to 1 kg, spring constant equal to 25 Newton/meter.Which damping constant b causes critical damping?If the damping constant b in the above system is set to 3 N ∙ sec/m, then what can be said about the number of timesdoes the object pass through its equilibrium position?If the damping constant b in the above system is set to 8 N ∙ sec/m, then what is the interval of time between thesecond time the object returns to its equilibrium position and the third time it returns to its equilibrium position?
Q2: A mercury thermometer having a time constant of 0.1 min is placed in a temperature bath at 100 F and allowed to come to equilibrium with the bath. At time t 0, the temperature of the bath begins to vary sinusoidally about its average temperature of 100 °F with an amplitude of 2 °F. If the frequency of oscillation is 10/T] cycles/min, derive the ultimate response equation of the thermometer reading as a function of time. What is phase lag?
An object of mass 0.5 kg is attached to a spring with the spring constant 8 N/m. The object oscillates with amplitude of 10 cm on a frictionless surface. At the time t 0, the object's location is measured at x = 0 as shown in the figure. a) Write the equation for x(t), v(t), and a(t). b) Calculate the time t when the object is at x = 6 cm. c) Calculate the velocity when the object is at x = 6 cm.
4 2. Determine the natural period of the system shown in Figure 2 using m = 3000 kg, k = 25 kN/m, L = 10 m, E = 200 GPa and I = 36(10) mm“. If the mass has initial displacement of 10 mm and initial velocity of 2 cm/s, plot the displacement and velocity response time-histories (using MS Excel or other program) and calculate the displacement and velocity at 2 s later if the system is (i) undamped, and (ii) damped with 3% damping ratio. El m Figure 2
A tuning fork is struck, producing a pure tone as its tines vibrate. The vibrations are modeled by the function v(t) = 0.7 sin(880t) where v(t) is the displacement of the tines in millimeters at time t seconds. Find the period of the vibration.
A tuning fork is struck, producing a pure tone as its tines vibrate. The vibrations are modeled by the function v(t) = 0.7 sin(880t) where u(t) is the displacement of the tines in millimeters at time t seconds. Find the frequency of the vibration, that is, the number of times the fork vibrates per second.
Q11 A:A 300g mass at the end of spring oscillates with an amplitude of 7 cm and a frequency of 1.8 Hz. 1-Find its maximum speed and maximum acceleration. 2-What is its speed when it is 3.0 cm from its equilibrium position?
Consider a harmonically forced m-c-k system shown below. The particular solution to the harmonic input force, ƒ (t) =F cos| x(1)=Xcos(1+0). F cos().is As the input frequency is varied, the response amplitude also varies. What is the maximum response amplitude (in meters)? Do not include units. Use scientific notation with three significant figures. Let m = 1 kg, c = 6 N-s/m, k = 112 N/m, and F = 111 N. Note that the numbers are chosen so that the maximum peak response exists (1-23²>0).
Q2. The system shown in Figure has a natural frequency of 5 Hz for the following data: m = 10 kg, Jo = 5 kg m²,r, initial displacement, the amplitude of free vibration is reduced by 80 percent in 10 cycles. Determine the values of k and c. = 10 cm, r, = 25 cm. When the system is disturbed by giving it an !! k Jo m
i, Consider the following 1-DOF system, where k :0-3 kg, calculate the natural frequency in rad/s and Hz. Also find the period of scillations and the maximum displacement if the spring isinitially displaced 10 am with no initial velocity. 857.8 N/m and m = 49.2 x

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