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)
A.
18 N/m
B.
12 N/m
C.
6 N/m
D.
9 N/m
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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 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)
A.
18 N/m
B.
12 N/m
C.
6 N/m
D.
24 N/m
Show solution
Solution
Frequency (f) = 1/(2π)√(k/m) => k = (2πf)²m = (2π × 3)² × 0.5 ≈ 18 N/m.
Correct Answer: A — 18 N/m
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Q. A mass-spring system oscillates with a frequency of 2 Hz. What is the period of oscillation? (2019)
A.
0.5 s
B.
1 s
C.
2 s
D.
4 s
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Solution
Period (T) = 1 / frequency = 1 / 2 Hz = 0.5 s.
Correct Answer: B — 1 s
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Q. A pendulum has a length of 1 m. What is its time period? (2023)
A.
2 s
B.
1 s
C.
0.5 s
D.
0.25 s
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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)
A.
0.00227 s
B.
0.0045 s
C.
0.01 s
D.
0.005 s
Show solution
Solution
Time period (T) = 1 / frequency = 1 / 440 Hz ≈ 0.00227 s
Correct Answer: A — 0.00227 s
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Q. A tuning fork vibrates at a frequency of 440 Hz. What is the time period of the tuning fork? (2020)
A.
0.00227 s
B.
0.0045 s
C.
0.01 s
D.
0.005 s
Show solution
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)
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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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. If the frequency of a simple harmonic oscillator is doubled, what happens to its period? (2021)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The period T is inversely proportional to frequency f. If f is doubled, T is halved.
Correct Answer: B — It halves
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Q. In a simple harmonic motion, the maximum velocity occurs at which point? (2019)
A.
At the mean position
B.
At the extreme position
C.
At half the amplitude
D.
At the equilibrium position
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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. In a simple harmonic motion, the restoring force is directly proportional to the displacement. What is the nature of this force? (2022)
A.
Conservative
B.
Non-conservative
C.
Frictional
D.
Centrifugal
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Solution
The restoring force in SHM is a conservative force as it can do work and store energy.
Correct Answer: A — Conservative
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Q. In a simple harmonic oscillator, if the mass is doubled, what happens to the time period? (2022)
A.
It remains the same
B.
It doubles
C.
It increases by √2
D.
It decreases by √2
Show solution
Solution
Time period (T) = 2π√(m/k), doubling m will double T.
Correct Answer: B — It doubles
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Q. In a simple harmonic oscillator, if the mass is increased, what happens to the time period? (2019)
A.
Increases
B.
Decreases
C.
Remains the same
D.
Depends on amplitude
Show solution
Solution
Time period (T) = 2π√(m/k). If mass (m) increases, T increases.
Correct Answer: A — Increases
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Q. The energy of a simple harmonic oscillator is maximum at which point? (2022)
A.
Mean position
B.
Amplitude
C.
Quarter amplitude
D.
Half amplitude
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Solution
The energy of a simple harmonic oscillator is maximum at the amplitude, where the velocity is zero and all energy is potential.
Correct Answer: B — Amplitude
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Q. The frequency of a simple harmonic oscillator is 5 Hz. What is its angular frequency? (2020)
A.
10 rad/s
B.
5 rad/s
C.
15 rad/s
D.
20 rad/s
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Solution
Angular frequency (ω) = 2πf = 2π × 5 = 10 rad/s
Correct Answer: A — 10 rad/s
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Q. The frequency of a wave is 10 Hz. What is the frequency of its second harmonic? (2021)
A.
5 Hz
B.
10 Hz
C.
20 Hz
D.
30 Hz
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Solution
The frequency of the second harmonic is twice the fundamental frequency. Therefore, if the fundamental frequency is 10 Hz, the second harmonic frequency is 2 * 10 Hz = 20 Hz.
Correct Answer: C — 20 Hz
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Q. The maximum displacement from the mean position in simple harmonic motion is called: (2019)
A.
Amplitude
B.
Frequency
C.
Wavelength
D.
Period
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Solution
The maximum displacement is defined as the amplitude.
Correct Answer: A — Amplitude
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Q. The maximum speed of a simple harmonic oscillator is 4 m/s. If the amplitude is 2 m, what is the angular frequency? (2019)
A.
2 rad/s
B.
4 rad/s
C.
1 rad/s
D.
8 rad/s
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Solution
Maximum speed (v_max) = ωA => ω = v_max / A = 4 m/s / 2 m = 2 rad/s.
Correct Answer: B — 4 rad/s
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Q. The restoring force in a simple harmonic oscillator is directly proportional to what? (2022)
A.
Displacement
B.
Velocity
C.
Acceleration
D.
Mass
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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. The restoring force in simple harmonic motion is directly proportional to what? (2022)
A.
Displacement
B.
Velocity
C.
Acceleration
D.
Mass
Show solution
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. The restoring force in simple harmonic motion is directly proportional to: (2023)
A.
Displacement
B.
Velocity
C.
Acceleration
D.
Mass
Show solution
Solution
Restoring force (F) is proportional to displacement (x), F = -kx.
Correct Answer: A — Displacement
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Q. What is the maximum displacement from the mean position in simple harmonic motion called? (2022)
A.
Amplitude
B.
Frequency
C.
Period
D.
Wavelength
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Solution
The maximum displacement from the mean position in simple harmonic motion is called the amplitude.
Correct Answer: A — Amplitude
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Q. What is the phase difference between two particles executing simple harmonic motion in phase? (2021)
A.
0 radians
B.
π/2 radians
C.
π radians
D.
3π/2 radians
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Solution
In phase means the phase difference is 0 radians.
Correct Answer: A — 0 radians
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Q. What is the phase difference between two particles executing simple harmonic motion in the same direction with the same amplitude and frequency? (2023)
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Solution
If two particles are executing simple harmonic motion in the same direction with the same amplitude and frequency, their phase difference is 0.
Correct Answer: A — 0
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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)
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Solution
If they have the same frequency and direction, the phase difference is 0.
Correct Answer: A — 0
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Q. What is the potential energy of a mass in simple harmonic motion at maximum displacement? (2023)
A.
Zero
B.
Maximum
C.
Minimum
D.
Depends on mass
Show solution
Solution
At maximum displacement, potential energy is maximum and kinetic energy is zero.
Correct Answer: B — Maximum
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