Oscillations & Waves - Oscillations
Q. A mass attached to a spring oscillates with a frequency of 3 Hz. What is the spring constant if the mass is 2 kg? (2023)
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A.
18 N/m
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B.
12 N/m
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C.
6 N/m
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D.
9 N/m
Solution
Frequency (f) = (1/2π)√(k/m) => k = (2πf)² * m = (2π*3)² * 2 ≈ 18 N/m.
Correct Answer: A — 18 N/m
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Q. A pendulum has a length of 1 m. What is its time period? (2023)
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A.
2 s
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B.
1 s
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C.
0.5 s
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D.
0.25 s
Solution
Time period (T) = 2π√(L/g) = 2π√(1/9.8) ≈ 2 s
Correct Answer: A — 2 s
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Q. A tuning fork vibrates at a frequency of 440 Hz. What is the time period of its vibration? (2020)
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A.
0.00227 s
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B.
0.0045 s
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C.
0.01 s
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D.
0.005 s
Solution
Time period (T) = 1 / frequency = 1 / 440 Hz ≈ 0.00227 s
Correct Answer: A — 0.00227 s
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Q. If the amplitude of a simple harmonic motion is doubled, what happens to the total energy of the system? (2022)
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A.
It remains the same
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B.
It doubles
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C.
It quadruples
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D.
It halves
Solution
Total energy (E) in SHM is proportional to the square of the amplitude (A). If A is doubled, E becomes 4A^2, hence it quadruples.
Correct Answer: C — It quadruples
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Q. In a simple harmonic motion, the maximum velocity occurs at which point? (2019)
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A.
At the mean position
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B.
At the extreme position
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C.
At half the amplitude
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D.
At the equilibrium position
Solution
Maximum velocity occurs at the mean position where the displacement is zero.
Correct Answer: A — At the mean position
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Q. The frequency of a simple harmonic oscillator is 5 Hz. What is its angular frequency? (2020)
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A.
10 rad/s
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B.
5 rad/s
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C.
15 rad/s
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D.
20 rad/s
Solution
Angular frequency (ω) = 2πf = 2π × 5 = 10 rad/s
Correct Answer: A — 10 rad/s
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Q. The restoring force in simple harmonic motion is directly proportional to what? (2022)
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A.
Displacement
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B.
Velocity
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C.
Acceleration
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D.
Mass
Solution
The restoring force (F) is directly proportional to the displacement (x) and acts in the opposite direction, F = -kx.
Correct Answer: A — Displacement
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Q. What is the phase difference between two particles executing simple harmonic motion in the same direction with the same frequency? (2021)
Solution
If they have the same frequency and direction, the phase difference is 0.
Correct Answer: A — 0
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