Quiz on Superposition of Harmonic Oscillations

What does the principle of superposition state?

• The sum of two solutions is not a solution.

• The resultant of two harmonic displacements is the vector sum of individual displacements.

• The resultant of two harmonic displacements is the product of individual displacements.

• The sum of two solutions is always zero.

What is the equation for a driven harmonic oscillator?

• m d²x/dt² = -kx - F(t)

• m d²x/dt² = kx - F(t)

• m d²x/dt² = kx + F(t)

• m d²x/dt² = -kx + F(t)

What is the form of the resultant displacement when two SHMs are combined?

• x = A + B

• x = A cos(!t + θ)

• x = A sin(!t + θ)

• x = A tan(!t + θ)

What happens to the amplitude of the resultant motion when two SHMs of slightly different frequencies are combined?

• It changes periodically.

• It doubles.

• It becomes zero.

• It remains constant.

What is the phenomenon called when two SHMs of slightly different frequencies are combined?

• Interference

• Damping

• Resonance

• Beats

If two SHMs have frequencies of 4Hz and 5Hz, what is the beat frequency?

• 4 Hz

• 3 Hz

• 2 Hz

• 1 Hz

What is the equation for the resultant motion of two SHMs with the same frequency?

• x = A cos(!t + θ)

• x = A sin(!t + θ)

• x = A + B

• x = A - B

What is the role of the phase angle in SHMs?

• It has no effect.

• It affects the amplitude.

• It determines the frequency.

• It shifts the wave in time.

What is the result of adding two SHMs of the same frequency but different amplitudes?

• A random motion.

• A constant motion.

• A simple harmonic motion.

• A non-harmonic motion.

What is the maximum value of the resultant amplitude when two SHMs are combined?

• a1 + a2

• a1 / a2

• a1 - a2

• a1 * a2