Q.1 A simple harmonic oscillator has a period of 2 seconds. What is its angular frequency?
π rad/s
2π rad/s
0.5π rad/s
4π rad/s
Explanation - Angular frequency ω = 2π/T. Substituting T = 2, ω = 2π/2 = π rad/s.
Correct answer is: π rad/s
Q.2 The time period of a simple pendulum depends on which factors?
Mass and length
Length and acceleration due to gravity
Mass and amplitude
Amplitude and length
Explanation - Time period of a pendulum, T = 2π√(L/g). It depends only on length L and gravitational acceleration g, not mass or amplitude (for small oscillations).
Correct answer is: Length and acceleration due to gravity
Q.3 A body executes SHM with amplitude 5 cm and maximum velocity 100 cm/s. The angular frequency of the motion is:
10 rad/s
20 rad/s
25 rad/s
15 rad/s
Explanation - Maximum velocity v_max = Aω. Hence, ω = v_max / A = 100 / 5 = 20 rad/s.
Correct answer is: 20 rad/s
Q.4 The potential energy in SHM is maximum when the displacement is:
Zero
Half of amplitude
Equal to amplitude
Twice the amplitude
Explanation - Potential energy is proportional to the square of displacement (U = ½kx²). It is maximum when x = A.
Correct answer is: Equal to amplitude
Q.5 A mass-spring system has a spring constant k = 200 N/m and mass m = 2 kg. Its frequency is:
5 Hz
2.52 Hz
3.18 Hz
1.59 Hz
Explanation - Frequency f = (1/2π)√(k/m). Substituting, f = (1/2π)√(200/2) = (1/2π)√100 = 1.59 Hz.
Correct answer is: 1.59 Hz
Q.6 The phase difference between velocity and displacement in SHM is:
0
π/2
π
π/4
Explanation - In SHM, velocity leads displacement by π/2 radians.
Correct answer is: π/2
Q.7 Which of the following is NOT a characteristic of simple harmonic motion?
Acceleration is proportional to displacement
Motion is periodic
Acceleration is directed away from mean position
Restoring force is proportional to displacement
Explanation - In SHM, acceleration is always directed towards the mean position, not away from it.
Correct answer is: Acceleration is directed away from mean position
Q.8 The total energy of a simple harmonic oscillator is:
Constant
Zero
Variable
Infinite
Explanation - The total energy remains constant, with potential and kinetic energy interchanging during the motion.
Correct answer is: Constant
Q.9 Two simple harmonic motions are represented by y1 = A sin(ωt) and y2 = A cos(ωt). The phase difference between them is:
π
π/2
0
2π
Explanation - Sine and cosine functions are out of phase by π/2 radians.
Correct answer is: π/2
Q.10 In a standing wave, the points of zero displacement are called:
Antinodes
Nodes
Loops
Crests
Explanation - Nodes are points where the displacement remains zero at all times in a standing wave.
Correct answer is: Nodes
Q.11 The speed of a wave on a string depends on:
Amplitude
Frequency
Tension and mass per unit length
Length of string only
Explanation - Wave speed v = √(T/μ), where T is tension and μ is mass per unit length.
Correct answer is: Tension and mass per unit length
Q.12 When two waves interfere destructively, the resultant amplitude is:
Sum of amplitudes
Zero
Difference of amplitudes
Product of amplitudes
Explanation - Destructive interference occurs when waves are out of phase by π radians, leading to amplitude = |A1 - A2|.
Correct answer is: Difference of amplitudes
Q.13 The frequency of the second harmonic of a vibrating string is:
Twice the fundamental frequency
Same as the fundamental frequency
Half the fundamental frequency
Four times the fundamental frequency
Explanation - The nth harmonic has frequency n times the fundamental frequency. For n = 2, it is twice the fundamental frequency.
Correct answer is: Twice the fundamental frequency
Q.14 If the amplitude of a simple harmonic motion is doubled, the total energy becomes:
Doubled
Halved
Quadrupled
Unchanged
Explanation - Total energy in SHM is proportional to A². Doubling amplitude makes energy four times greater.
Correct answer is: Quadrupled
Q.15 A tuning fork produces a sound of frequency 256 Hz. The wavelength of the sound in air (speed = 340 m/s) is:
1.33 m
0.75 m
1.25 m
0.65 m
Explanation - Wavelength λ = v/f = 340 / 256 ≈ 1.33 m.
Correct answer is: 1.33 m
Q.16 The displacement of a particle in SHM is given by x = 10 sin(100πt). The frequency of oscillation is:
25 Hz
50 Hz
75 Hz
100 Hz
Explanation - ω = 100π = 2πf → f = 50 Hz.
Correct answer is: 50 Hz
Q.17 In resonance, the amplitude of the driven system is:
Maximum
Minimum
Zero
Constant
Explanation - At resonance, the natural frequency equals the driving frequency, leading to maximum amplitude.
Correct answer is: Maximum
Q.18 Which quantity remains the same in all harmonics of a vibrating string?
Frequency
Amplitude
Wave speed
Wavelength
Explanation - Wave speed depends only on tension and linear mass density, so it remains constant for all harmonics.
Correct answer is: Wave speed
Q.19 The quality factor (Q) of a damped oscillator is:
Ratio of energy stored to energy lost per cycle
Energy lost per cycle
Total energy of system
Ratio of frequency to time period
Explanation - Q measures the sharpness of resonance, defined as the ratio of energy stored to energy dissipated per cycle.
Correct answer is: Ratio of energy stored to energy lost per cycle
Q.20 If two waves of equal amplitude and frequency travel in opposite directions, they produce:
A progressive wave
No wave
A standing wave
A shock wave
Explanation - Opposite direction waves of equal amplitude and frequency superimpose to form a standing wave.
Correct answer is: A standing wave
Q.21 In a progressive wave, energy is:
Not transmitted
Transmitted along the medium
Stored at a point
Lost completely
Explanation - In progressive waves, energy moves forward through the medium.
Correct answer is: Transmitted along the medium
Q.22 For a particle in SHM, the maximum kinetic energy occurs when:
Displacement is maximum
Displacement is zero
Velocity is zero
Acceleration is maximum
Explanation - Kinetic energy is maximum when potential energy is zero, i.e., at mean position where displacement = 0.
Correct answer is: Displacement is zero
Q.23 Two waves are in phase if their phase difference is:
π/2
π
0 or 2π
3π/2
Explanation - In-phase condition occurs when phase difference is zero or an integral multiple of 2π.
Correct answer is: 0 or 2π
Q.24 The equation of a progressive wave is y = 0.05 sin(4πt - πx). The wavelength is:
2 m
1 m
4 m
0.5 m
Explanation - Wave equation is y = A sin(ωt - kx). Here, k = π → λ = 2π/k = 2 m.
Correct answer is: 2 m