A 5.00-kg object oscillates on a spring with a force constant of 150 N/m. The damping coefficient is 0.200 kg/s. The system is driven by a sinusoidal force of maximum value 50.0 N, and an angular frequency of 20.0 rad/s. What is the amplitude A of the oscillations? A = If the driving angular frequency is varied, at what angular frequency o will resonance occur? rad/s
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- A mass m = 3.3 kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A = 4.5 cm and a frequency f = 1.5 Hz. a. Write an equation for the spring constant k. b. Calculate the spring constant k, in Newtons per meter. c. Write an equation for the total mechanical energy, E, of the motion. Your expression should be in terms of the variables in the original problem statement. d. Calculate the total mechanical energy E, in joules.A string has length 2.0 m, tension 60 N, and linear density 0.080 kg/m. The left end of the string is connected to a massless ring that slides on a frictionless pole, and the ring is attached to a spring of stiffness 150 N/m. The right end is attached to a massless ring that slides on a frictionless pole. The left end of the string is driven by a transverse force of amplitude 4.0 N and frequency 21 Hz. F(t) S x = 0 x = L 2. The input mechanical impedance (at x = 0) is Zmo = s/im + ipLc tan(kL). Using established impedances (do not calculate), explain why the input impedance is given by this expression. Evaluate the impedance for the specified values of the system. Be sure to show the units. Note: In the computation of the tangent, do not round off the value of k. From the value of the impedance, determine the steady-state velocity amplitude (in m/s) of the left ring.A rubber ball and a clay ball have equal mass and are dropped onto a digital scale. The rubber ball bounces back to nearly the same height. The clay ball sticks to the scale when it hits. For the (single) interaction with the scale…a. What is the ratio of the change of the rubber ball’s momentum to the change of the clay ball’s momentum? ∆???????∆?????= ______________________________b. What is the ratio of the impulse imparted to the rubber ball to the impulse imparted to the clay ball? ????????????= ______________________________c. Which of the following graphs could represent, to the same scale, the force exerted by the scale on each ball as a function of time? Select an answer for the rubber ball and an answer for the clay ball. A)B)C)D)E)rubber ball: ____________clay ball: ___________ *Please write an detail as much as possible
- A large block with mass 18 kg executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency 1.27 Hz. Block smaller block with mass 5 kg rests on it, as shown in the figure, and the coefficient of static friction between the two is flg = 0.401. The acceleration of gravity is 9.8 m/s². k -0000² 25 5 kg s=0.401 18 kg What maximum amplitude of oscillation can the system have if the block is not to slip? Answer in units of cm.IC-3 A 167 gram mass is vibrating about its equilibrium position on the end of a spring as shown in problem SHM-8. While vibrating, the mass is observed to have a maximum speed of 0.500m/s and a maximum acceleration of 6.00m/s. At t0 the mass is at the equilibrium position with a velocity to the left. a) Find the numerical values for the angular frequency o and the amplitude of the motion xm. Hint: think about how Vm and xm are related. b) Find the value of the spring constant of the spring. c) The position of the block is described by x Xmcos(@t+0,). Find all possible values of 0, and then explain how to determine the value of 0, that corresponds to the given conditions. 99+ hpA 2.50-kg object is attached to a spring with a force constant of 4.50 N/m. The object rests on a horizontal surface that has a viscous, oily substance spread evenly on it. The object is pulled 15.0 cm to the right of the equilibrium position and set into harmonic motion. After ?1=2.00 s the amplitude has fallen to 7.00 cm due to frictional losses in the oil. Calculate the natural frequency f0 of the system. Calculate the frequency ? of oscillation that will be observed for the motion.
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