2021/4/27 14:40 P. 4 m (20 seconds) (a) 0.2 (c) 12 (b) 20 (d) 0.4 43. The ratio of the unit of acceleration and velocity 49, gives the unit of the physical quantity (a) Time (b) Frequency (c) Amplitude (d) Speed 44. A bus moves with uniform velocity along a straight line path. If the average velocity of the bus is 80 km

2021/4/27 14:40 P. 4 m (20 seconds) (a) 0.2 (c) 12 (b) 20 (d) 0.4 43. The ratio of the unit of acceleration and velocity 49, gives the unit of the physical quantity (a) Time (b) Frequency (c) Amplitude (d) Speed 44. A bus moves with uniform velocity along a straight line path. If the average velocity of the bus is 80 km

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter16: Oscillations

Section: Chapter Questions

Problem 9PQ: A simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its...

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An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.
An object of mass m moves in simple harmonic motion with amplitude 12.0 cm on a light spring. Its maximum acceleration is 108 cm/s2. Regard m as a variable. (a) Find the period T of the object. (b) Find its frequency f. (c) Find the maximum speed vmax of the object. (d) Find the total energy E of the objectspring system. (e) Find the force constant k of the spring. (f) Describe the pattern of dependence of each of the quantities T, f, vmax, E, and k on m.
A car of mass 2.00 103 kg is lowered by 1.50 cm when four passengers, each of mass 70.0 kg, sit down in it. a. Determine the damping constant b of the shock absorbers that will provide critical damping. b. Suppose for the same car the shock absorbers are so worn that they provide almost no damping. Find the period of up-and-down oscillation of the car after hitting a bump in the road.
Engineering Application Each piston of an engine makes a sharp sound every other revolution of the engine. (a) How fast is a race car going if its eight—cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? (b) At how many revolutions per minute is the engine rotating?
Four people, each with a mass of 72.4 kg, are in a car with a mass of 1 130 kg. An earthquake strikes. The vertical oscillations of the ground surface make the car bounce up and down on its suspension springs, but the driver manages to pull off the road and stop. When the frequency of the shaking is 1.80 Hz, the car exhibits a maximum amplitude of vibration. The earthquake ends, and the four people leave the car as fast as they can. By what distance docs the cars undamaged suspension lift the cars body as the people get out?
A baby bounces up and down in her crib. Her mass is 12.5 kg, and the crib mattress can be modeled as a light spring with force constant 700 N/m. (a) The baby soon learns to bounce with maximum amplitude and minimum effort by bending her knees at what frequency? (b) If she were to use the mattress as a trampoline losing contact with it for part of each cyclewhat minimum amplitude of oscillation does she require?
A 500-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.0 cm. Calculate the maximum value of its (a) speed and (b) acceleration, (c) the speed and (d) the acceleration when the object is 6.00 cm from the equilibrium position, and (e) the time interval required for the object to move from x = 0 to x = 8.00 cm.
A simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its position to change from x = A to x = A/2 in terms of the period T.
The equations listed in Table 2.2 give position as a function of time, velocity as a function of time, and velocity as a function of position for an object moving in a straight line with constant acceleration. The quantity vxi appears in every equation. (a) Do any of these equations apply to an object moving in a straight line with simple harmonic motion? (b) Using a similar format, make a table of equations describing simple harmonic motion. Include equations giving acceleration as a function of time and acceleration as a function of position. State the equations in such a form that they apply equally to a blockspring system, to a pendulum, and to other vibrating systems. (c) What quantity appears in every equation?
A simple pendulum has mass 1.20 kg and length 0.700 m. (a) What is the period of the pendulum near the surface of Earth? (b) If the same mass is attached to a spring, what spring constant would result in the period of motion found in part (a)?
A simple pendulum is suspended from the ceiling of a stationary elevator, and the period is determined, (i) When the elevator accelerates upward, is the period (a) greater, (b) smaller, or (c) unchanged? (ii) When the elevator has a downward acceleration, is the period (a) greater, (b) smaller, or (c) unchanged? (iii) When the elevator moves with constant upward velocity, is the period of the pendulum (a) greater, (b) smaller, or (c) unchanged?
An object of mass m is hung from a spring and set into oscillation. The period of the oscillation is measured and recorded as T. The object of mass m is removed and replaced with an object of mass 2m. When this object is set into oscillation, what is the period of the motion? (a) 2T (b) 2T (c) T (d) T/2 (e) T/2