Free Simple Harmonic Motion MCQs with Answers

1. Simple harmonic motion is defined as motion in which the acceleration is

• A. constant in magnitude and direction
• B. proportional to the displacement and directed towards the mean position
• C. proportional to the speed
• D. always zero at the extreme positions

Explanation: The restoring force is proportional to the displacement and always points back to equilibrium, which produces sinusoidal motion in time. Acceleration is therefore greatest at the extremes, where displacement is maximum, and zero at the mean position, where the speed is greatest. A mass on a spring and a simple pendulum at small angles are the standard examples.

2. In simple harmonic motion, the speed of the body is maximum

• A. at the extreme positions
• B. at the mean position
• C. midway between mean and extreme
• D. everywhere, since it is constant

Explanation: At the mean position the displacement is zero, so all the energy is kinetic and the speed peaks, while at the extremes the body is momentarily at rest with all the energy stored as potential. The total energy stays constant throughout, simply exchanging between the two forms twice every cycle. Acceleration follows the opposite pattern to speed.

3. The time period of a simple pendulum depends on

• A. its mass and length
• B. its length and the acceleration due to gravity
• C. its amplitude, for all amplitudes
• D. the material of the bob

Explanation: The period is 2 pi times the square root of length divided by g, so it is independent of the mass entirely and of the amplitude provided the swing is small. Lengthening the pendulum four times doubles the period. This independence from mass is what makes the pendulum a reliable timekeeper and a good way to measure g.

4. Resonance occurs when

• A. the driving frequency equals the natural frequency of the system
• B. the driving frequency is much higher than the natural frequency
• C. the amplitude is very small
• D. there is no damping present at all

Explanation: At resonance energy is transferred most efficiently to the oscillator and the amplitude builds to a large value, limited only by damping. It explains why a radio can be tuned to one station, why a wine glass can be shattered by a sung note, and why marching troops break step on a bridge. Damping reduces the peak amplitude but does not abolish the effect.

5. The energy of a simple harmonic oscillation depends upon the

• A. Frequency
• B. Time period
• C. Wavelength
• D. Amplitude

Explanation: This is the option marked correct in the official UHS answer key, and the total energy of a simple harmonic oscillator is proportional to the square of the amplitude, so doubling the amplitude quadruples the energy. Strictly the energy also depends on the square of the frequency, since the expression is half m omega squared A squared, but amplitude is the variable the question is pointing at. The energy stays constant through the cycle, merely exchanging between kinetic and potential forms.