The pendulum shown below consists of a uniform disk with radius r = 2.35 cm and a mass of 460 grams. The disk is supported in a vertical plane by a pivot located d 1.75 cm from the center of the disk. Pivot• R a. What is the frequency of oscillation if the disk is displaced by a small angle and released? Hz b. What is the frequency of oscillation if the mass of the disk is and then displaced by a small angle and released? Hz
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- A mass is attached to the end of a spring. Then it is displaces 4.00cm from its equilibrium position. In the next 0.500 s, the mass moves through its equilibrium position, stops 4.00cm on the other side, then returns to its original displacement. It continues to vibrate at this rate. What are its amplitude,period, and frequency?An object stretches a spring 6 inches in equilibrium. a) Find its displacement for t> 0 if it is initially displaced 4 inches below equilibrium and given a downward velocity of 8 ft/s. y(t) b) State the natural frequency of the oscillation. Wo = rad/s = c) State the period of the oscillation. T S = d) State the amplitude of the oscillation. R ft e) State the phase angle of the oscillation. The phase angle should be between π radians. Φ = Notes: 1. Use g rad = 32 ft/sec². 2. Upward forces and movement are associated with y > 0. Downward forces and movement are associated with y < 0. π andQuestions 6-13 refer to the figure below. The graph represents the position as a function of time for a small 1.20 kg object attached to a light spring that is oscillating on a smooth horizontal surface. n 0.4 Time (s) 0 0.2 6. What is the amplitude of the motion (in cm)? 7. What is the period of the motion (in s)? 8. What is the frequency of the motion (in Hz)? 9. What is the angular frequency of the motion (in rad/s)? 0.6 11. What is the maximum speed of the object (in m/s)? 10. What is the spring constant of the spring (in N/m)? (Be aware of units!) 0.8 12. What is the maximum acceleration of the object (in m/s²)? 13. If instead of attaching the 1.20 kg mass to the spring, we attach a mass of 2.4 kg. What is the new period (in s) of the motion?
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- In the figure, a physical pendulum consists of a uniform solid disk (of radius R = 56.2 cm) supported in a vertical plane by a pivot located a distance d = 22.8 cm from the center of the disk. The disk is displaced by a small angle and released. What is the period of the resulting simple harmonic motion? Number i Units Pivot R 12A pendulum that consists of two uniform rings, the first ring has Radius R = 12 cm and mass 2.5kg, and the second ring has radius r= 7cm and mass 1.6kg. Both rings are attached to a rod of mass 0.15kg. The pendulum swings freely about frictionless pivot o. If the pendulum is to have a period of 2.2 a for small oscillations, what must be the rod length L?The pendulum shown below consists of a uniform disk with radius r = 2.35 cm and a mass of 410 grams. The disk is supported in a vertical plane by a pivot located d = 1.75 cm from the center of the disk. Pivot• d R. a. What is the frequency of oscillation if the disk is displaced by a small angle and released? Hz b. What is the frequency of oscillation if the mass of the disk is and then displaced by a small angle and released? Hz