Q.1 Which of the following is a necessary condition for a motion to be simple harmonic?
Acceleration is constant
Acceleration is proportional to velocity
Acceleration is proportional to displacement and directed towards mean position
Velocity is constant
Explanation - In SHM, the restoring acceleration is directly proportional to the displacement from the mean position and always directed towards it.
Correct answer is: Acceleration is proportional to displacement and directed towards mean position
Q.2 The time period of a simple pendulum depends on:
Amplitude of oscillation
Length of the pendulum
Mass of the bob
Material of the bob
Explanation - For small oscillations, the time period of a simple pendulum is T = 2π√(L/g), depending only on its length and acceleration due to gravity.
Correct answer is: Length of the pendulum
Q.3 A particle executing SHM has maximum velocity when:
At mean position
At extreme position
At half of amplitude
Velocity is constant throughout
Explanation - In SHM, the velocity is maximum at the mean position and zero at the extreme positions.
Correct answer is: At mean position
Q.4 The graph between acceleration and displacement in SHM is:
A straight line with positive slope
A straight line with negative slope
A parabola
A circle
Explanation - In SHM, a = –ω²x, so the graph between acceleration and displacement is a straight line with a negative slope.
Correct answer is: A straight line with negative slope
Q.5 If the amplitude of SHM is doubled, then the maximum acceleration becomes:
Half
Double
Four times
Unchanged
Explanation - Maximum acceleration is a_max = ω²A. If amplitude doubles, maximum acceleration also doubles.
Correct answer is: Double
Q.6 In SHM, potential energy is maximum at:
Mean position
Extreme position
Half of amplitude
Everywhere
Explanation - Potential energy is maximum when displacement is maximum i.e., at the extreme positions.
Correct answer is: Extreme position
Q.7 The phase difference between velocity and displacement in SHM is:
0
π/2
π
2π
Explanation - Velocity leads displacement by π/2 in SHM.
Correct answer is: π/2
Q.8 The kinetic energy of a body in SHM is maximum at:
Mean position
Extreme position
Half amplitude
None of these
Explanation - At mean position velocity is maximum, hence kinetic energy is maximum.
Correct answer is: Mean position
Q.9 The restoring force in SHM is given by:
F = –kx
F = –mv
F = –mg
F = ma
Explanation - In SHM, restoring force is proportional to displacement and opposite in direction, F = –kx.
Correct answer is: F = –kx
Q.10 If the length of a pendulum is increased four times, its period will:
Remain same
Double
Halve
Become four times
Explanation - Period T ∝ √L. If length becomes 4L, T becomes 2T.
Correct answer is: Double
Q.11 For a particle in SHM, the acceleration is zero when:
At extreme position
At mean position
At half amplitude
Everywhere
Explanation - Acceleration a = –ω²x. At mean position x=0, so a=0.
Correct answer is: At mean position
Q.12 The energy of a particle in SHM is proportional to:
Amplitude
Amplitude squared
Displacement
Velocity
Explanation - Total energy in SHM is E = ½kA², hence proportional to the square of amplitude.
Correct answer is: Amplitude squared
Q.13 If frequency of SHM is doubled, angular frequency becomes:
Same
Double
Four times
Halved
Explanation - Angular frequency ω = 2πf. If f is doubled, ω also doubles.
Correct answer is: Double
Q.14 Displacement in SHM is given by x = A cos(ωt + φ). Here φ is:
Amplitude
Frequency
Phase constant
Time period
Explanation - φ is the initial phase constant determining the starting position of oscillation.
Correct answer is: Phase constant
Q.15 The maximum speed of a particle in SHM is given by:
Aω²
Aω
ω
A/ω
Explanation - Maximum speed is vmax = Aω, where A is amplitude and ω is angular frequency.
Correct answer is: Aω
Q.16 In SHM, the velocity is zero at:
Mean position
Extreme positions
Half amplitude
Everywhere
Explanation - Velocity becomes zero at maximum displacement (extreme positions).
Correct answer is: Extreme positions
Q.17 If a body of mass m executes SHM with angular frequency ω, its maximum kinetic energy is:
½mω²A²
mωA²
½mA²
mA²/ω²
Explanation - Kinetic energy is maximum at mean position: KE_max = ½mv²max = ½m(ωA)² = ½mω²A².
Correct answer is: ½mω²A²
Q.18 If amplitude of SHM is increased, the time period:
Increases
Decreases
Remains constant
Becomes half
Explanation - Time period T = 2π√(m/k) is independent of amplitude.
Correct answer is: Remains constant
Q.19 The average kinetic energy over a complete cycle of SHM is:
Zero
½ Total energy
Total energy
¼ Total energy
Explanation - In SHM, average kinetic energy over one cycle equals average potential energy, each equal to half of total energy.
Correct answer is: ½ Total energy
Q.20 If the frequency of a simple pendulum on earth is f, then its frequency on moon will be (g_moon = g/6):
f/√6
f√6
6f
f/6
Explanation - Frequency f ∝ √g. On moon, f' = f√(g_moon/g) = f√(1/6).
Correct answer is: f/√6
Q.21 The total energy in SHM is:
Constant
Variable
Zero
Depends on displacement
Explanation - The sum of kinetic and potential energies remains constant in SHM.
Correct answer is: Constant
Q.22 At what displacement is the kinetic energy equal to potential energy in SHM?
x = A/√2
x = A/2
x = A
x = 0
Explanation - When KE = PE, displacement is x = A/√2.
Correct answer is: x = A/√2
Q.23 A body oscillates with time period T. Its maximum speed is proportional to:
1/T
T
1/T²
T²
Explanation - Maximum speed v = Aω = A(2π/T), hence proportional to 1/T.
Correct answer is: 1/T
Q.24 Which of the following is NOT a characteristic of SHM?
Periodicity
Restoring force proportional to displacement
Velocity always constant
Total energy constant
Explanation - Velocity is not constant in SHM; it varies with position.
Correct answer is: Velocity always constant
Q.25 In SHM, velocity and acceleration are:
In same phase
In opposite phase
90° out of phase
180° out of phase
Explanation - Velocity leads displacement by π/2, while acceleration lags displacement by π/2, so velocity and acceleration are 90° out of phase.
Correct answer is: 90° out of phase