Simple Harmonic Motion
Q. In a simple harmonic oscillator, if the maximum speed is 4 m/s and the amplitude is 2 m, what is the angular frequency?
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A.
2 rad/s
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B.
4 rad/s
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C.
6 rad/s
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D.
8 rad/s
Solution
Maximum speed (v_max) = ωA. Thus, ω = v_max/A = 4/2 = 2 rad/s.
Correct Answer: B — 4 rad/s
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Q. In simple harmonic motion, the acceleration is maximum when the displacement is:
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A.
Maximum
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B.
Zero
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C.
Negative maximum
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D.
None of the above
Solution
In SHM, acceleration is maximum at maximum displacement (A).
Correct Answer: A — Maximum
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Q. In simple harmonic motion, the acceleration of the particle is maximum when it is at which position?
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A.
Mean position
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B.
Amplitude
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C.
Halfway to amplitude
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D.
None of the above
Solution
In SHM, acceleration is maximum at the amplitude (maximum displacement).
Correct Answer: B — Amplitude
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Q. In simple harmonic motion, the maximum displacement from the mean position is called what?
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A.
Amplitude
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B.
Frequency
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C.
Period
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D.
Wavelength
Solution
The maximum displacement from the mean position in simple harmonic motion is called amplitude.
Correct Answer: A — Amplitude
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Q. In simple harmonic motion, the maximum speed occurs at which point?
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A.
At the mean position
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B.
At the amplitude
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C.
At one-fourth of the amplitude
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D.
At three-fourths of the amplitude
Solution
The maximum speed in SHM occurs at the mean position where the displacement is zero.
Correct Answer: A — At the mean position
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Q. In simple harmonic motion, the restoring force is directly proportional to which of the following?
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A.
Displacement
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B.
Velocity
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C.
Acceleration
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D.
Mass
Solution
The restoring force is directly proportional to the displacement from the mean position.
Correct Answer: A — Displacement
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Q. In simple harmonic motion, the total mechanical energy is conserved. What forms of energy are involved?
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A.
Kinetic and Potential Energy
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B.
Kinetic and Thermal Energy
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C.
Potential and Thermal Energy
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D.
Only Kinetic Energy
Solution
In SHM, the total mechanical energy is the sum of kinetic and potential energy, which remains constant.
Correct Answer: A — Kinetic and Potential Energy
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Q. In simple harmonic motion, the velocity of the particle is maximum when it is at which position?
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A.
Mean position
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B.
Maximum displacement
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C.
Equilibrium position
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D.
None of the above
Solution
In simple harmonic motion, the velocity is maximum at the mean position where the displacement is zero.
Correct Answer: A — Mean position
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Q. The displacement of a simple harmonic oscillator is given by x(t) = A cos(ωt + φ). What is the maximum displacement?
Solution
The maximum displacement in SHM is equal to the amplitude A.
Correct Answer: A — A
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Q. The equation of motion for a simple harmonic oscillator is given by x(t) = A cos(ωt + φ). What does φ represent?
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A.
Amplitude
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B.
Phase constant
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C.
Angular frequency
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D.
Time period
Solution
In the equation of motion for simple harmonic motion, φ is the phase constant, which determines the initial position of the oscillator.
Correct Answer: B — Phase constant
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Q. The equation of motion for a simple harmonic oscillator is given by x(t) = A cos(ωt + φ). What does A represent?
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A.
Angular frequency
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B.
Phase constant
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C.
Amplitude
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D.
Displacement
Solution
A represents the amplitude of the oscillation, which is the maximum displacement from the mean position.
Correct Answer: C — Amplitude
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Q. The restoring force in a simple harmonic motion is directly proportional to:
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A.
Displacement
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B.
Velocity
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C.
Time
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D.
Mass
Solution
Restoring force F = -kx, where k is the spring constant and x is the displacement.
Correct Answer: A — Displacement
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Q. The time period of a simple harmonic oscillator is given by T = 2π√(m/k). If the mass is doubled, what will be the new time period?
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A.
T
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B.
2T
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C.
√2 T
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D.
T/√2
Solution
If the mass is doubled, the new time period T' = 2π√(2m/k) = √2 * (2π√(m/k)) = √2 * T. Thus, the time period increases.
Correct Answer: B — 2T
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Q. The total energy in a simple harmonic oscillator is given by which of the following?
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A.
1/2 kA^2
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B.
kA
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C.
mgh
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D.
1/2 mv^2
Solution
Total energy E = 1/2 kA^2, where A is the amplitude.
Correct Answer: A — 1/2 kA^2
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Q. The total mechanical energy in a simple harmonic oscillator is given by which of the following?
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A.
1/2 kA^2
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B.
1/2 mv^2
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C.
kA
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D.
mv^2
Solution
Total mechanical energy in SHM is E = 1/2 kA^2, where A is the amplitude.
Correct Answer: A — 1/2 kA^2
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Q. What is the equation of motion for a simple harmonic oscillator with amplitude A and angular frequency ω?
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A.
x(t) = A cos(ωt)
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B.
x(t) = A sin(ωt)
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C.
x(t) = A e^(ωt)
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D.
x(t) = A ωt
Solution
The equation of motion for SHM is x(t) = A cos(ωt) or x(t) = A sin(ωt).
Correct Answer: A — x(t) = A cos(ωt)
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Q. What is the phase difference between the displacement and acceleration in simple harmonic motion?
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A.
0 degrees
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B.
90 degrees
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C.
180 degrees
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D.
270 degrees
Solution
In simple harmonic motion, acceleration is always opposite to displacement, hence the phase difference is 180 degrees.
Correct Answer: C — 180 degrees
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Q. What is the phase difference between the displacement and acceleration of a particle in simple harmonic motion?
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A.
0 degrees
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B.
90 degrees
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C.
180 degrees
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D.
270 degrees
Solution
In simple harmonic motion, the acceleration is always directed towards the mean position and is 180 degrees out of phase with the displacement.
Correct Answer: C — 180 degrees
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Q. What is the phase difference between the displacement and acceleration of a simple harmonic oscillator?
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A.
0 degrees
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B.
90 degrees
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C.
180 degrees
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D.
270 degrees
Solution
In simple harmonic motion, acceleration is 180 degrees out of phase with displacement.
Correct Answer: C — 180 degrees
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Q. What is the potential energy stored in a spring when it is compressed by a distance x?
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A.
1/2 kx
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B.
1/2 kx²
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C.
kx
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D.
kx²
Solution
The potential energy (PE) stored in a spring is given by PE = 1/2 kx², where k is the spring constant and x is the displacement.
Correct Answer: B — 1/2 kx²
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Q. What is the relationship between the frequency and the period of a simple harmonic oscillator?
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A.
f = T
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B.
f = 1/T
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C.
f = T^2
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D.
f = 2T
Solution
The frequency (f) is the reciprocal of the period (T), so f = 1/T.
Correct Answer: B — f = 1/T
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Q. What is the relationship between the period and frequency of a simple harmonic oscillator?
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A.
T = f
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B.
T = 1/f
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C.
T = f^2
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D.
T = 2f
Solution
The period (T) is the reciprocal of frequency (f), so T = 1/f.
Correct Answer: B — T = 1/f
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Q. What is the relationship between the period of a simple harmonic oscillator and its mass and spring constant?
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A.
T = 2π√(m/k)
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B.
T = 2π√(k/m)
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C.
T = m/k
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D.
T = k/m
Solution
The period T of a mass-spring system is given by T = 2π√(m/k).
Correct Answer: A — T = 2π√(m/k)
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Q. What is the relationship between the potential energy and kinetic energy in simple harmonic motion at maximum displacement?
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A.
PE = KE
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B.
PE > KE
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C.
PE < KE
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D.
PE = 0
Solution
At maximum displacement, all energy is potential energy (PE), and kinetic energy (KE) is zero.
Correct Answer: B — PE > KE
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