1. a Piano String Sounds a Middle a by Vibrating Primarily at 220 Hz
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Physics 111 HW24 assigned 2 May 2011
1. A piano string sounds a middle A by vibrating primarily at 220 Hz. a) Calculate its period and angular frequency. b) Calculate the period and angular frequency for a soprano singing a “high A,” two octaves up, which is four times the frequency of the piano string. (You double the frequency for each octave you go up.)
2. If an object on a horizontal frictionless surface is attached to a spring, displaced, and then released, it will oscillate. If it is displaced 0.120 m from its equilibrium position and released with zero initial speed, then after 0.800 s its displacement is found to be 0.120 m on the opposite side, and it has passed the equilibrium position once during this interval. Find the amplitude, period, and frequency.
3. The displacement of an oscillating object as a function of time is shown in the figure at right. What is the frequency, amplitude, and period?
4. A harmonic oscillator is made by using a 0.600 kg frictionless block and an ideal spring of unknown force constant. The oscillator is found to have a period of 0.150 s. Find the force constant of the spring.
5. A 42.5-kg chair is attached to a spring and allowed to oscillate. When the chair is empty the chair takes 1.30s to make one complete vibration. But with a person sitting in it, with her feet off the floor, the chair now takes 2.54 s for one cycle. What is the mass of the person?
6. A 2.00 kg mass executes simple harmonic oscillation with an amplitude of 5.00 cm. The maximum speed of the mass is 2.00 m/s. a) Find the frequency of the oscillation in Hz. b) If the mass is at x = 0m when t = 0s, find x(t).
7. The motion of the piston of an automobile engine is approximately simple harmonic. a) If the stroke of an engine (twice the amplitude) is 0.100 m and the engine runs at 3500 rev/min, compute the acceleration of the piston at the endpoint of its stroke. b) If the piston has mass 0.450 kg, what net force must be exerted on it at this point?