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Chapter 15
Oscillatory Motion

Conceptual Problems

1. A body of mass 5.0 kg is suspended by a spring which stretches 10 cm when the mass is attached. It is then displaced downward an additional 5.0 cm and released. Its position as a function of time is approximately

a. y = .10 sin 9.9t
b. y = .10 cos 9.9t
c. y = .10 cos (9.9t + .1)
d. y = .10 sin (9.9t + 5)e. y = .05 cos 9.9t

2. A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation x = 5.0 sin (πt). The acceleration (in m/s2) of the body at t = 1.0 s is approximately

a. 3.5
b. 49
c. 14
d. 43
e. 4.3

3. A body oscillates with simple harmonic motion along the x axis. Its displacementvaries with time according to the equation x = 5 sin (πt + π/3). The phase (in rad) of the motion at t = 2 s is

a. 7π/3
b. π/3
c. π
d. 5π/3
e. 2π

4. A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5.0 sin (πt + π/3). The velocity (in m/s) of the body at t = 1.0 s is

a. +8.0b. –8.0
c. –14
d. +14
e. –5.0

5. The motion of a particle connected to a spring is described by x = 10 sin (πt). At what time (in s) is the potential energy equal to the kinetic energy?

a. 0
b. 0.25
c. 0.50
d. 0.79
e. 1.0

6. The amplitude of a system moving with simple harmonic motion is doubled. The total energy will then bea. 4 times larger
b. 3 times larger
c. 2 times larger
d. the same as it was
e. half as much

7. A mass m = 2.0 kg is attached to a spring having a force constant k = 290 N/m as in the figure. The mass is displaced from its equilibrium position and released. Its frequency of oscillation (in Hz) is approximately

[pic]

a. 12
b. 0.50c. 0.01
d. 1.9
e. 0.08

8. The mass in the figure slides on a frictionless surface. If m = 2 kg, k1 = 800 N/m and k2 = 500 N/m, the frequency of oscillation (in Hz) is approximately

[pic]

a. 6
b. 2
c. 4
d. 8
e. 10

9. Two circus clowns (each having a mass of 50 kg) swing on two flying trapezes (negligible mass, length 25 m) shownin the figure. At the peak of the swing, one grabs the other, and the two swing back to one platform. The time for the forward and return motion is

[pic]

a. 10 s
b. 50 s
c. 15 s
d. 20 s
e. 25 s

10. A uniform rod (mass m = 1.0 kg and length L = 2.0 m) pivoted at one end oscillates in a vertical plane as shown below. The period of oscillation (in s) isapproximately

[pic]

a. 4.0
b. 1.6
c. 3.2
d. 2.3
e. 2.0

11. A horizontal plank (m = 2.0 kg, L = 1.0 m) is pivoted at one end. A spring (k = 1.0 ( 103 N/m) is attached at the other end, as shown in the figure. Find the angular frequency (in rad/s) for small oscillations.

[pic]

a. 39
b. 44
c. 55
d. 66
e.25

12. The figure shows a uniform rod (length L = 1.0 m, mass = 2.0 kg) suspended from a pivot a distance d = 0.25 m above its center of mass. The angular frequency (in rad/s) for small oscillations is approximately

[pic]

a. 1.0
b. 2.5
c. 1.5
d. 4.1
e. 3.5

13. In the figure below, a disk (radius R = 1.0 m, mass = 2.0 kg) is suspended from a pivota distance d = 0.25 m above its center of mass. The angular frequency (in rad/s) for small oscillations is approximately

[pic]

a. 4.2
b. 2.1
c. 1.5
d. 1.0
e. 3.8

14. In the figure below, a hoop (radius R = 1.0 m, mass = 2.0 kg) having four spokes of negligible mass is suspended from a pivot a distance d = .25 m above its center of mass. The...
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