physics : class11 Acceleration-Time Function : Periodic Functions : Oscillations and Waves MCQ Questions and Answers
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Acceleration-Time Function
MCQ questions and answers.
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MCQ Questions
1. For simple harmonic motion, the acceleration-time function is generally represented by which form?
A.
a(t) = A sin(ωt + φ)
B.
a(t) = A cos(ωt + φ)
C.
a(t) = A t
D.
a(t) = A/t
Correct Answer:
a(t) = A cos(ωt + φ)
Explanation:
In simple harmonic motion, acceleration varies sinusoidally with time and can be written as a(t) = A cos(ωt + φ), where A is the maximum acceleration and φ is the phase constant.
2. If the acceleration-time function is a(t) = 4 cos(2t) m/s², what is the maximum acceleration?
A.
2 m/s²
B.
4 m/s²
C.
6 m/s²
D.
8 m/s²
Correct Answer:
4 m/s²
Explanation:
The maximum acceleration is the amplitude of the acceleration-time function. In a(t) = 4 cos(2t), the amplitude is 4 m/s².
3. For the acceleration function a(t) = 3 sin(πt) m/s², what is the angular frequency?
A.
π/2 rad/s
B.
π rad/s
C.
2π rad/s
D.
3π rad/s
Correct Answer:
π rad/s
Explanation:
Comparing a(t) = 3 sin(πt) with a(t) = A sin(ωt), the coefficient of t is the angular frequency. Therefore, ω = π rad/s.
4. What is the period of the acceleration function a(t) = 5 cos(2πt) m/s²?
A.
0.25 s
B.
0.5 s
C.
1 s
D.
2 s
Correct Answer:
1 s
Explanation:
The period is T = 2π/ω. Here, ω = 2π rad/s, so T = 2π/(2π) = 1 s.
5. At what values can the acceleration in simple harmonic motion lie if its maximum value is a_max?
A.
Only between 0 and a_max
B.
Only between -a_max and 0
C.
Between -a_max and +a_max
D.
Only at a_max
Correct Answer:
Between -a_max and +a_max
Explanation:
Because acceleration varies sinusoidally with time, its value ranges from the negative maximum, -a_max, to the positive maximum, +a_max.
6. If a(t) = 6 cos(πt) m/s², what is the acceleration at t = 0 s?
A.
0 m/s²
B.
3 m/s²
C.
6 m/s²
D.
-6 m/s²
Correct Answer:
6 m/s²
Explanation:
At t = 0, a(0) = 6 cos(0) = 6 × 1 = 6 m/s².
7. For a(t) = 8 sin(πt) m/s², what is the acceleration at t = 0 s?
A.
0 m/s²
B.
4 m/s²
C.
8 m/s²
D.
-8 m/s²
Correct Answer:
0 m/s²
Explanation:
At t = 0, a(0) = 8 sin(0) = 0 m/s².
8. In the acceleration-time function a(t) = 10 cos(4t + φ), what does φ represent?
A.
Maximum acceleration
B.
Angular frequency
C.
Phase constant
D.
Time period
Correct Answer:
Phase constant
Explanation:
In a sinusoidal acceleration function, φ is the phase constant. It determines the initial phase or starting condition of the acceleration.
9. If the period of an acceleration-time function is 2 s, what is its angular frequency?
A.
π/2 rad/s
B.
π rad/s
C.
2π rad/s
D.
4π rad/s
Correct Answer:
π rad/s
Explanation:
Angular frequency is given by ω = 2π/T. For T = 2 s, ω = 2π/2 = π rad/s.
10. For the acceleration function a(t) = -5 cos(3t) m/s², what is the minimum acceleration?
A.
-10 m/s²
B.
-5 m/s²
C.
0 m/s²
D.
5 m/s²
Correct Answer:
-5 m/s²
Explanation:
The amplitude of the function is 5 m/s², so the acceleration ranges from -5 m/s² to +5 m/s². Hence, the minimum acceleration is -5 m/s².
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