1. For a particle undergoing simple harmonic motion, the displacement-time function is x = A sin(ωt). What does A represent?
A.
Amplitude of the motion
B.
Angular frequency
C.
Time period
D.
Initial displacement only
Correct Answer:
Amplitude of the motion
Explanation:
In the displacement-time function x = A sin(ωt), A is the maximum displacement from the mean position, called the amplitude.
2. Which of the following is a periodic displacement-time function?
A.
x = 5t
B.
x = 5t²
C.
x = 5 sin(2t)
D.
x = 5 + t
Correct Answer:
x = 5 sin(2t)
Explanation:
A sine function repeats its values after equal intervals of time, so x = 5 sin(2t) represents a periodic displacement.
3. The displacement-time function of a particle is x = 4 cos(πt). What is the amplitude?
A.
π units
B.
4 units
C.
2 units
D.
1/π units
Correct Answer:
4 units
Explanation:
The amplitude is the coefficient of the cosine function. Therefore, for x = 4 cos(πt), the amplitude is 4 units.
4. For the displacement function x = A sin(ωt), the displacement at t = 0 is:
A.
A
B.
−A
C.
0
D.
ω
Correct Answer:
0
Explanation:
At t = 0, x = A sin(0) = 0. Thus, the particle has zero displacement at that instant.
5. A particle has displacement x = 3 cos(2πt) metres. What is its maximum displacement from the mean position?
A.
π metres
B.
2π metres
C.
3 metres
D.
6π metres
Correct Answer:
3 metres
Explanation:
The maximum value of the displacement is the amplitude, which is the coefficient 3 in the given function.
6. If the displacement-time function is x = A cos(ωt), the displacement at t = 0 is:
A.
0
B.
A
C.
−A
D.
ωA
Correct Answer:
A
Explanation:
At t = 0, x = A cos(0) = A. Hence, the initial displacement is equal to the amplitude.
7. The displacement-time function x = 2 sin(4t) has an amplitude of:
A.
2 units
B.
4 units
C.
6 units
D.
8 units
Correct Answer:
2 units
Explanation:
In x = A sin(ωt), the coefficient of the sine function is the amplitude. Here, A = 2 units.
8. A displacement-time graph for periodic motion repeats itself after 5 seconds. What is the time period of the motion?
A.
2.5 seconds
B.
5 seconds
C.
10 seconds
D.
1 second
Correct Answer:
5 seconds
Explanation:
The time period is the smallest time interval after which the displacement-time graph repeats its pattern. Therefore, it is 5 seconds.
9. For the displacement function x = 6 sin(πt), the greatest possible displacement is:
A.
−6 units
B.
0 units
C.
6 units
D.
π units
Correct Answer:
6 units
Explanation:
The amplitude of x = 6 sin(πt) is 6 units, so the greatest positive displacement is 6 units.
10. Which function represents a particle whose displacement varies periodically with time and has amplitude 5 units?
A.
x = 5 sin(3t)
B.
x = 3 sin(5t)
C.
x = 5t
D.
x = t² + 5
Correct Answer:
x = 5 sin(3t)
Explanation:
The sine function gives periodic variation, and its coefficient 5 gives the amplitude. Thus, x = 5 sin(3t) has amplitude 5 units.
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