Chapter 11 - Oscillations n Waves Flashcards
What is the restoring force?
If the mass is moved either to the left, which compresses the spring, or to the right, which stretches it, the spring exerts a force on the mass that acts in the direction of returning the mass to the equilibrium position; hence it is called a restoring force
State the relationship between value of k and external force and stiffness
The greater the value of k, the greater the force needed to stretch a spring a given distance. That is, the stiffer the spring, the greater the spring constant k.
How is the amplitude found in SHM?
The maximum displacement—the greatest distance from
the equilibrium point—is called the amplitude,
How is the period found in SHM?
the time required to complete one cycle
How is the frequency found in SHM?
the number of complete cycles per second
What does simple harmonic motion mean?
Any oscillating system for which the net restoring force is directly propor- tional to the negative of the displacement (as in Eq. 11–1, F = –kx) is said to exhibit simple harmonic motion (SHM)
What is total mechanical energy of SHM proportional to the square of the amplitude?
As the mass oscillates back and forth, the energy continuously changes from potential energy to kinetic energy, and back again (Fig. 11–5). At the extreme points, x = – A and x = A (Fig. 11–5a, c), all the energy is stored in the spring as potential energy (and is the same whether the spring is com- pressed or stretched to the full amplitude). At these extreme points, the mass stops for an instant as it changes direction, so v = 0 and
E = 1m(0)^2 + 1kA^2 = 1kA^2.
Doubling the amplitude. Suppose the spring in Fig. 11–5 is stretched twice as far (to x = 2A). What happens to (a) the energy of the system, (b) the maximum velocity of the oscillating mass, (c) the maximum acceleration of the mass?
a) From Eq. 11–4a, the total energy is proportional to the square of the amplitude A, so stretching it twice as far quadruples the energy (22 = 4). You may protest, “I did work stretching the spring from x = 0 to x = A. Don’t I do the same work stretching it from A to 2A?” No. The force you exert is proportional to the displacement x, so for the second displacement, from x = A to 2A, you do more work than for the first displacement (x = 0 to A).
Doubling the amplitude. Suppose the spring in Fig. 11–5 is stretched twice as far (to x = 2A). What happens to (c) the maximum acceleration of the mass?
c) Since the force is twice as great when we stretch the spring twice as far(F = kx), the acceleration is also twice as great: a r F r x.
Doubling the amplitude. Suppose the spring in Fig. 11–5 is stretched twice as far (to x = 2A). What happens to (b) the maximum velocity of the oscillating mass,
b) From Eq. 11–5a, we can see that when the amplitude is doubled, the maxi- mum velocity must be doubled.
What is the relationship between mass, period and k?
We see that the larger the mass, the longer the period; and the stiffer the spring (larger k), the shorter the period.
Why is a pendulum not shm? (2)
Since F is proportional to the sine of u and not to u itself, the motion is not SHM.
Because a pendulum does not undergo precisely SHM, the period does depend slightly on the amplitude—the more so for large amplitudes
Is the velocity of a wave moving along a rope the same as the velocity of a particle of the rope?
o. The two velocities are different, both in magnitude and direc- tion. The wave on the rope of Fig. 11–22 moves to the right along the tabletop, but each piece of the rope only vibrates to and fro, perpendicular to the traveling wave. (The rope clearly does not travel in the direction that the wave on it does.)
How do you find the wavelength in periodic sinusoidal wave?
The distance between two successive crests is the wavelength
How do you find the frequency in periodic sinusoidal wave?
The frequency, f, is the number of crests—or complete cycles—that pass a given point per unit time.
