Simple Harmonic Motion

Simple Harmonic Motion MDCAT MCQs with answers

22 past paper MCQs on Simple Harmonic Motion, from the Waves unit of MDCAT Physics. The year each question appeared is shown where known; tap “Show answer” for the correct option and a short solution.

Read the notes first Practise the unit as a quiz

1.When will the oscillations of a pendulum stop in the absence of resistive forces? (MDCAT 2022)

  1. never
  2. after 10 minutes
  3. in 10 minutes
  4. immediately
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Correct answer: (a) never

With nothing to take its energy away the motion is undamped and continues indefinitely.

2.Reducing the mass $M$ of a suspended body to one fourth will change the frequency of oscillation to: (MDCAT 2022)

  1. one fourth
  2. double
  3. quadruple
  4. half
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Correct answer: (b) double

$f=\dfrac{1}{2\pi}\sqrt{k/m}$, so a quarter of the mass doubles the frequency.

3.If the length of a second's pendulum becomes four times, then its time period will become: (MDCAT 2023)

  1. four times
  2. two times
  3. half
  4. one fourth
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Correct answer: (b) two times

$T=2\pi\sqrt{l/g}$, so $T$ goes as the square root of the length.

4.The energy of a Simple Harmonic oscillation depends upon the: (UHS MDCAT 2025)

  1. frequency
  2. time period
  3. wavelength
  4. amplitude
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Correct answer: (d) amplitude

The total energy of an oscillator is $\tfrac12 k x_0^2$, which depends on the amplitude alone.

5.When a particle executing simple harmonic motion moves from the mean position to the extreme position, its kinetic energy: (KMU MDCAT 2025)

  1. Increases continuously
  2. Decreases continuously and becomes zero at the extreme position
  3. Remains constant throughout the motion
  4. Becomes maximum at the extreme position
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Correct answer: (b) Decreases continuously and becomes zero at the extreme position

The speed falls to zero at the extreme position, and with it the kinetic energy.

6.Body mass 10kg, spring k=20 N/m, max displacement 20cm. Acceleration is: (NUMS MDCAT 2024)

  1. 2.2 ms−2
  2. 4 ms−2
  3. 2 ms−2
  4. 0.4 ms−2
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Correct answer: (d) 0.4 ms−2

$a=kx/m=20\times0.2/10$, which is $0.4\,\mathrm{m\,s^{-2}}$.

7.When will the oscillations stop in the absence of resistive forces? (UHS MDCAT 2023)

  1. Never
  2. After 10 minutes
  3. In 10 minutes
  4. Immediately
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Correct answer: (a) Never

With nothing to take energy from it, an oscillator would go on for ever.

8.Reducing mass M of a suspending body to one fourth will change the frequency of oscillation to (UHS MDCAT 2023)

  1. One fourth
  2. Double
  3. Quadrupule
  4. Half
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Correct answer: (b) Double

The frequency goes as $1/\sqrt{m}$, so a quarter of the mass doubles it.

9.If the length of second pendulum becomes four times, then its time period will become: (UHS MDCAT 2023)

  1. Four times
  2. Two times
  3. Half
  4. One fourth
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Correct answer: (b) Two times

$T=2\pi\sqrt{l/g}$ goes as the square root of the length, so four times the length doubles the period.

10.Potential energy of a spring at the equilibrium position is: (PMC MDCAT 2022)

  1. Zero
  2. Infinite
  3. Maximum
  4. Information is Insufficient
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Correct answer: (a) Zero

At the equilibrium position the spring is unstretched, so it stores nothing.

11.Two springs having force constants in the ratio of 3:4, both the springs are stretched by equal force F, if elongation in first spring is x then elongation in the second spring is: (PMC MDCAT 2022)

  1. 3x
  2. 4x
  3. 3x/4
  4. 4x/3
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Correct answer: (c) 3x/4

$x=F/k$, so the stiffer spring stretches less, in the ratio $3/4$.

12.Kinetic energy of an oscillating simple pendulum at the equilibrium position is: (PMC MDCAT 2022)

  1. Maximum
  2. Minimum
  3. Zero
  4. Information insufficient
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Correct answer: (a) Maximum

The bob moves fastest as it passes through the mean position.

13.If the period of oscillation of man (M) suspended from a spring is 1s, then the period of 16M will be: (NUMS MDCAT 2022)

  1. 1s
  2. 2s
  3. 3s
  4. 4s
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Correct answer: (d) 4s

$T$ goes as $\sqrt{m}$, so sixteen times the mass gives four times the period.

14.The pendulum of a certain pendulum clock is made of brass. When the temperature increases, what happens to the period of the clock? (PMC Practice 2021)

  1. It increases
  2. It decreases
  3. It remains the same
  4. It decreases with the square of temperature
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Correct answer: (a) It increases

The brass rod lengthens as it warms, and $T=2\pi\sqrt{l/g}$ grows with the length.

15.When the length of simple pendulum is doubled, the ratio of its new time period to old time period is: (UHS MDCAT 2019)

  1. 3√2
  2. 1√2
  3. 2√2
  4. √2
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Correct answer: (d) √2

$T=2\pi\sqrt{l/g}$ goes as the square root of the length.

16.In simple harmonic motion, acceleration will be maximum, when object is at: (UHS MDCAT 2019)

  1. Maximum displacement from the mean position
  2. Center position
  3. Half of the maximum displacement from mean position
  4. Mean position
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Correct answer: (a) Maximum displacement from the mean position

$a=-\omega^2x$, so the acceleration is greatest where the displacement is greatest.

17.In SHM the kinetic energy of the body is maximum when: (UHS MDCAT 2018)

  1. The body is at mean position
  2. The body is at extreme position from the mean
  3. The body is exactly half way down between mean and extreme position
  4. The body is somewhere between mean and extreme position
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Correct answer: (a) The body is at mean position

The speed is greatest as the body passes the mean position.

18.When the frequency of the applied force becomes equal to one of natural frequencies of body then the body oscillates with maximum displacement this phenomenon is called: (UHS MDCAT 2018)

  1. Heating
  2. Resonance
  3. Reverbnation
  4. Damping
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Correct answer: (b) Resonance

Driving a body at its own natural frequency is resonance.

19.The velocity and acceleration of a particle performing S.H.M. have a steady phase relationship. The acceleration showed a phase lead over the the velocity of: (UHS MDCAT 2017)

  1. π
  2. π/2
  3. -π/2
  4. -π
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Correct answer: (b) π/2

The acceleration leads the velocity by a quarter of a cycle.

20.A particle executes S.H.M. with frequency f. The frequency of variation of its maximum or minimum kinetic energy is: (UHS MDCAT 2017)

  1. f/2
  2. f
  3. 2f
  4. 4f
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Correct answer: (c) 2f

The kinetic energy passes through its maximum twice in each cycle, so it varies at $2f$.

21.The vertical extension in a light spring by a weight of 1 kg suspended from the wire is 9.8 cm, the period of the oscillation is: (UHS MDCAT 2017)

  1. 20pi sec
  2. 2pi sec
  3. 2pi/10 sec
  4. 200pi sec
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Correct answer: (c) 2pi/10 sec

$k=mg/x=9.8/0.098=100\,\mathrm{N\,m^{-1}}$, so $T=2\pi\sqrt{1/100}$, that is $2\pi/10\,\mathrm{s}$.

22.Resonance occurs when the driving frequency is: (UHS MDCAT 2016)

  1. Greater than natural frequency
  2. Unequal the natural frequency
  3. Less than natural frequency
  4. Equal to the natural frequency
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Correct answer: (d) Equal to the natural frequency

Resonance comes when the driving frequency matches a natural frequency of the body.

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