Q. If the mass of a simple harmonic oscillator is tripled, how does the frequency change?
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A.
It triples
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B.
It is halved
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C.
It is reduced to one-third
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D.
It remains the same
Solution
The frequency f is inversely proportional to the square root of the mass m, so if m is tripled, the frequency is reduced to one-third.
Correct Answer:
C
— It is reduced to one-third
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Q. If the spring constant of a spring is doubled, how does the period of the simple harmonic motion change?
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A.
It doubles
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B.
It is halved
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C.
It remains the same
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D.
It quadruples
Solution
The period T is inversely proportional to the square root of the spring constant k. If k is doubled, the period is halved.
Correct Answer:
B
— It is halved
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Q. In simple harmonic motion, what is the maximum displacement from the equilibrium position called?
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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 equilibrium position in simple harmonic motion is called the amplitude.
Correct Answer:
A
— Amplitude
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Q. In simple harmonic motion, what type of energy is at its maximum when the displacement is at its maximum?
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A.
Kinetic energy
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B.
Potential energy
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C.
Total energy
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D.
Mechanical energy
Solution
At maximum displacement, the potential energy is at its maximum while kinetic energy is zero.
Correct Answer:
B
— Potential energy
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Q. What is the acceleration of an object in simple harmonic motion at maximum displacement?
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A.
Zero
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B.
Maximum
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C.
Minimum
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D.
Constant
Solution
The acceleration is maximum at maximum displacement, directed towards the equilibrium position.
Correct Answer:
B
— Maximum
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Q. What is the formula for the period of a simple harmonic oscillator?
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A.
T = 2π√(m/k)
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B.
T = 2π√(k/m)
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C.
T = 2π(m/k)
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D.
T = 2π(k/m)
Solution
The period T of a simple harmonic oscillator is given by T = 2π√(m/k), where m is the mass and k is the spring constant.
Correct Answer:
B
— T = 2π√(k/m)
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Q. What is the phase constant in simple harmonic motion?
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A.
It determines the amplitude
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B.
It determines the frequency
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C.
It determines the initial position and direction
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D.
It has no effect
Solution
The phase constant φ determines the initial position and direction of the motion in simple harmonic motion.
Correct Answer:
C
— It determines the initial position and direction
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Q. What is the relationship between frequency and period in simple harmonic motion?
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A.
Frequency = Period × 2π
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B.
Frequency = 1/Period
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C.
Frequency = Period/2
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D.
Frequency = Period × 4
Solution
Frequency is the reciprocal of the period, so Frequency = 1/Period.
Correct Answer:
B
— Frequency = 1/Period
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Q. What is the total mechanical energy in a simple harmonic oscillator?
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A.
E = 1/2 k A^2
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B.
E = 1/2 m v^2
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C.
E = k A
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D.
E = m g h
Solution
The total mechanical energy in a simple harmonic oscillator is given by E = 1/2 k A^2, where A is the amplitude and k is the spring constant.
Correct Answer:
A
— E = 1/2 k A^2
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Q. Which of the following equations represents the position of a simple harmonic oscillator as a function of time?
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A.
x(t) = A cos(ωt + φ)
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B.
x(t) = A sin(ωt + φ)
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C.
x(t) = A e^(ωt)
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D.
x(t) = A t^2
Solution
The position of a simple harmonic oscillator can be represented as x(t) = A cos(ωt + φ) or x(t) = A sin(ωt + φ).
Correct Answer:
A
— x(t) = A cos(ωt + φ)
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