Oscillations & Waves - Oscillations

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Q1. A mass attached to a spring oscillates with a frequency of 3 Hz. What is the spring constant if the mass is 0.5 kg? (2022)

Solution:

Frequency (f) = 1/(2π)√(k/m) => k = (2πf)²m = (2π × 3)² × 0.5 ≈ 18 N/m.

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Q2. The maximum speed of a simple harmonic oscillator is 4 m/s. If the amplitude is 2 m, what is the angular frequency? (2019)

Solution:

Maximum speed (v_max) = ωA => ω = v_max / A = 4 m/s / 2 m = 2 rad/s.

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Q3. What is the maximum displacement from the mean position in simple harmonic motion called? (2022)

Solution:

The maximum displacement from the mean position in simple harmonic motion is called the amplitude.

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Q4. If the amplitude of a simple harmonic motion is doubled, what happens to the total energy of the system? (2022)

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.

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Q5. The restoring force in simple harmonic motion is directly proportional to what? (2022)

Solution:

The restoring force (F) is directly proportional to the displacement (x) and acts in the opposite direction, F = -kx.

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Q6. 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)

Solution:

Frequency (f) = (1/2π)√(k/m) => k = (2πf)² * m = (2π*3)² * 2 ≈ 18 N/m.

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Q7. A tuning fork vibrates at a frequency of 440 Hz. What is the time period of its vibration? (2020)

Solution:

Time period (T) = 1 / frequency = 1 / 440 Hz ≈ 0.00227 s

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Q8. In a simple harmonic motion, the restoring force is directly proportional to the displacement. What is the nature of this force? (2022)

Solution:

The restoring force in SHM is a conservative force as it can do work and store energy.

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Q9. A pendulum has a length of 1 m. What is its time period? (2023)

Solution:

Time period (T) = 2π√(L/g) = 2π√(1/9.8) ≈ 2 s

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Q10. The maximum displacement from the mean position in simple harmonic motion is called: (2019)

Solution:

The maximum displacement is defined as the amplitude.