The phase angle
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- In circular motion vr=0 vr=v theta vr=-v theta ar=0arrow_forwardQUESTION 2 Vibration absorber (also called tuned mass damper) is used to reduce* the vibration at the natural frequency of the original system. Consider a M-K system shown below. Original System x(t) Modified System x₁(1) X2(t) K M F(t) K M m F(t) absorber K This system has a natural frequency at rad. The absorber mass and the spring are attached to the original system as shown in the figure, and the values are selected so that (1) the amplitude of the original mass, M, at M the original natural frequency is zero, and (2) the new natural frequencies are moved away from the original natural frequency. The selection of absorber mass and stiffness, m and k, is easy. They have the same ratio as the ratio of the original system. That is, M/m = KIK. Find the transfer functions X1(s)/F(s) and X2(s)/F(s) before you can answer questions. * I said "reduce," but for undamped system, it can be completely eliminated. What is the response amplitude (particular solution only) of the second mass if…arrow_forwardA 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.arrow_forward
- 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?arrow_forwardChoose correct answer: An object is in simple harmonic motion . The angular acceleration is 20 rad/s2 . When the angular velocity is 2 rad/s, the displacement of the object is Select one: 5 m 40 m 0.2 m 10 marrow_forwardQUESTION 2 Consider a two-degrees-of-freedom system shown below. k₁ woo kz oooo kz oooo m2 F2 What is the amplitude of vibration of mass 1 oscillating at the input frequency? (This is just another way of asking for the amplitude of the particular solution). The answer must be positive. Use scientific notation with 3 significant figures. Omit units. Use m1 = 1 kg m2 = 1 kg k1 = 127 N/m k2 = 106 N/m k3 = 169 N/m F1 230 cos(1.7t) N F2 = 0.arrow_forward
- An electrical switch gear is supported by a crane through a steel cable of length 4 m and diameter 0.01 m. If the natural time period of the axial vibration of the switch gear is found to be o.o1 s, find the stiffness of the switch cable. * O 4 MN/m O 5 MN/m O 2 MN/m З MN/marrow_forwardThe string of a piano is made of music wire. The wire has a mass of 150 grams and a length of 1.5 m. The tension in the wire is 110000 N. The fundamental natural frequency of the string approximately is. * (2 Points) 150 Hz 350 Hz 450 Hz 250 Hz Meeting now 1516 None of the mentionedarrow_forwardA block-spring system oscillates in a simple harmonic motion on a frictionless horizontal table. Its displacement varies with time according to x(t) = 0.2 cos(2t - n/4). The earliest time the particle reaches position x = 0.1 m isarrow_forward
- An industrial press is mounted on a rubber pad to be isolated from its foundation. If the rubber pad is compressed 5 mm by the self-weight of the press, find the natural frequency of the system. 7.1 rad/s 44.3 rad/s 34.8 rad/s 9.4 rad/sarrow_forwardMechanical vibrations problem: If one of the components of the harmonic motion x(t) = 10 sin(ωt + 60°) is x1(t) = 5 sin (ωt + 30°), find the other component.arrow_forwardQUESTION 3 Vibration absorber (also called tuned mass damper) is used to reduce* the vibration at the natural frequency of the original system. Consider a M-K system shown below. Original System x(t) Modified System x₁(1) X2(t) K K MA M 0000 M F(1) F(t) absorber K This system has a natural frequency at rad. The absorber mass and the spring are attached to the original system as shown in the figure, and the values are selected so that (1) the amplitude of the original mass, M. at the original natural frequency is zero, and (2) the new natural frequencies are moved away from the original natural frequency. The selection of absorber mass and stiffness, m and k, is easy. They have the same ratio as the ratio of the original system. That is, M/m = Klk. Find the transfer functions X1(s)/F(s) and X2(s)/F(s) before you can answer questions. What is the fundamental frequency (first natural frequency) of the modified system in rad/s? Use scientific notation with 3 signifincant figures. Omit…arrow_forward
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