Q1. What is the potential energy of a mass in simple harmonic motion at maximum displacement? (2023)
Solution:
At maximum displacement, potential energy is maximum and kinetic energy is zero.
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Q2. The maximum displacement from the mean position in simple harmonic motion is called: (2019)
Solution:
The maximum displacement is defined as the amplitude.
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Q3. A tuning fork vibrates at a frequency of 440 Hz. What is the time period of the tuning fork? (2020)
Solution:
Time period (T) = 1 / frequency = 1 / 440 Hz ≈ 0.00227 s.
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Q4. In a simple harmonic oscillator, if the mass is increased, what happens to the time period? (2019)
Solution:
Time period (T) = 2π√(m/k). If mass (m) increases, T increases.
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Q5. In a simple harmonic motion, the maximum velocity occurs at which point? (2019)
Solution:
Maximum velocity occurs at the mean position where the displacement is zero.
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Q6. What is the phase difference between two particles executing simple harmonic motion in the same direction with the same amplitude and frequency? (2023)
Solution:
If two particles are executing simple harmonic motion in the same direction with the same amplitude and frequency, their phase difference is 0.
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Q7. The restoring force in simple harmonic motion is directly proportional to: (2023)
Solution:
Restoring force (F) is proportional to displacement (x), F = -kx.
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Q8. 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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Q9. A mass-spring system oscillates with a frequency of 2 Hz. What is the period of oscillation? (2019)
Solution:
Period (T) = 1 / frequency = 1 / 2 Hz = 0.5 s.
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Q10. 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.
