Explain resonance reactions and the concept of resonance.
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- 9. Solve the coupled oscillator system such that m₁ = m² = 1, k₁ = k3 = 9,k₂ = 8. Assume the first mass is pushed 2 units to the right of equilibrium and the 2nd 2 units to the left of equilibrium, with zero initial velocities. Describe the behavior of the motions of the masses at each of the nodes.If you shake a magnetic compass e and then set it down, you can watch the needle bounce back and forth around its equilibrium position. If this motion is unimpeded by friction, it is an example of simple harmonic motion 2. You may learn more about simple harmonic motion in Phys 1230, but we'll be seeing another example soon in Unit 8. In this case, energy is being transferred continually between magnetic potential energy and kinetic energy, and the energy is conserved if there is no friction. When there is no kinetic energy, the needle is the maximally deflected and its magnetic potential energy is maximum; when the magnetic potential energy is minimum, the needle is moving the fastest. Conservation of energy shows that KE (0) +U (0) = Umax (functions of angle, not multiplication). For your compass, the measured angle between maximum deflection and equilibrium is 58°. What percent of the maximum kinetic energy does the needle have when it is only deflected 29° from equilibrium? Give…What is the component of F along axis AB?
- B74) A variable-speed electric motor, having an unbalance, is mounted on an isolator. As the speed of the motor is increased from zero, the amplitudes of vibration of the motor have been observed to be 0.55 inches at resonance and 0.15 inches at speeds much greater than resonance. Find the numerical value of the damping ratio of the isolator.