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1.) A mass m = 5.00 kg is suspended from a spring and oscillates according to the equation of motion x(t) = 0.500 cos(5.00 t + /4). What is the

1.) A mass m = 5.00 kg is suspended from a spring and oscillates according to the equation of motion x(t) = 0.500 cos(5.00t +π/4). What is the spring constant?

2.) A mass of 10.0 kg is hanging by a steel wire 1.00 m long and 1.00 mm in diameter. If the mass is pulled down slightly and released, what will be the frequency of the resulting oscillations? Young's modulus for steel is 2.0·1011 N/m^2.

3.) When a mass is attached to a vertical spring, the spring is stretched a distance d. The mass is then pulled down from this position and released. It undergoes 50.0 oscillations in 30.0 s. What was the distance d?

4.) A vertical spring with a spring constant of 2.00 N/m has a 0.300-kg mass attached to it, and the mass moves in a medium with a damping constant of 0.0250 kg/s. The mass is released from rest at a position 5.00 cm from the equilibrium position. How long will it take for the amplitude to decrease to 2.50 cm?

5.) Imagine you are an astronaut who has landed on another planet and wants to determine the free-fall acceleration on that planet. In one of the experiments you decide to conduct, you use a pendulum 0.500 m long and find that the period of oscillation for this pendulum is 1.50 s. What is the acceleration due to gravity on that planet?

6.) Two pendulums with identical lengths of 1.000 m are suspended from the ceiling and begin swinging at the same time. One is at Manila, in the Philippines, where g = 9.784 m/s^2, and the other is at Oslo, Norway, where g = 9.819 m/s^2. After how many oscillations of the Manila pendulum will the two pendulums be in phase again? How long will it take for them to be in phase again?

7.) Two sources, A and B, emit a sound of a certain wavelength. The sound emitted from both sources is detected at a point away from the sources. The sound from source A is a distance d from the observation point, whereas the sound from source B has to travel a distance of 3λ. What is the largest value of the wavelength, in terms of d, for the maximum sound intensity to be detected at the observation point? If d = 10.0 m and the speed of sound is 340. m/s, what is the frequency of the emitted sound?

8.) A policeman with a very good ear and a good understanding of the Doppler effect stands on the shoulder of a freeway assisting a crew in a 40-mph work zone. He notices a car approaching that is honking its horn. As the car gets closer, the policeman hears the sound of the horn as a distinct B4 tone (494 Hz). The instant the car passes by, he hears the sound as a distinct A4 tone (440 Hz). He immediately jumps on his motorcycle, stops the car, and gives the motorist a speeding ticket. Explain his reasoning.

9.) A train whistle emits a sound at a frequency f = 3000. Hz when stationary. You are standing near the tracks when the train goes by at a speed of v = 30.0 m/s. What is the magnitude of the change in the frequency (|Δf|) of the whistle as the train passes? (Assume that the speed of sound is v = 343 m/s.)

10.) You are driving along a highway at 30.0 m/s when you hear a siren. You look in the rear-view mirror and see a police car approaching you from behind with a constant speed. The frequency of the siren that you hear is 1300. Hz. Right after the police car passes you, the frequency of the siren that you hear is 1280. Hz.

a)          How fast was the police car moving?              

b)          You are so nervous after the police car passes you that you pull off the road and stop. Then you hear another siren, this time from an ambulancen approaching from behind. The frequency of its siren that you hear is 1400. Hz. Once it passes, the frequency is 1200. Hz. What is the actual frequency of the ambulance's siren?

11.) A bat flying toward a wall at a speed of 7.00 m/s emits an ultrasound wave with a frequency of 30.0 kHz. What frequency does the reflected wave have when it reaches the flying bat?

12.) Two trains are traveling toward each other in still air at 25.0 m/s relative to the ground. One train is blowing a whistle at 300. Hz. Assume that the speed of sound is 343 m/s.

a)          What frequency is heard by a man on the ground facing the whistle-blowing train?              
b)          What frequency is heard by a man on the other train?
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