Simple Harmonic Motion Challenge

Question 1

For a mass–spring oscillator, which change would double the period if all other factors remain constant?

Accepted Answer

Quadrupling the mass

Answer

Halving the mass

Answer

Quadrupling the spring constant

Answer

Doubling the spring constant

Question 2

In ideal simple harmonic motion, when is the magnitude of acceleration greatest?

Accepted Answer

At the turning points

Answer

At the equilibrium position

Answer

Halfway between equilibrium and an extreme

Answer

Whenever velocity is maximum

Question 3

A particle in SHM passes through equilibrium moving in the positive direction. Which quantity must be zero at that instant?

Accepted Answer

Displacement

Answer

Kinetic energy

Answer

Speed

Answer

Jerk

Question 4

Which graph is always 90 degrees out of phase with displacement in ideal SHM?

Accepted Answer

Velocity versus time

Answer

Potential energy versus time

Answer

Kinetic energy versus time

Answer

Total energy versus time

Question 5

A pendulum undergoes small-angle oscillations on Earth. Which modification increases its frequency?

Accepted Answer

Shortening the length

Answer

Increasing the bob mass

Answer

Increasing the initial angle slightly

Answer

Using a denser bob of the same shape

Question 6

In SHM described by x = A cos(ωt + φ), what does φ represent?

Accepted Answer

The initial phase constant

Answer

The angular momentum

Answer

The restoring force coefficient

Answer

The energy loss rate

Question 7

Which statement best describes the restoring force in ideal simple harmonic motion?

Accepted Answer

It is proportional to displacement and opposite in direction

Answer

It is constant in magnitude and always inward

Answer

It is proportional to velocity and opposite in direction

Answer

It is largest at equilibrium and zero at extremes

Question 8

If the amplitude of an ideal mass–spring oscillator is doubled, what happens to its total mechanical energy?

Accepted Answer

It becomes four times as large

Answer

It doubles

Answer

It stays the same

Answer

It becomes eight times as large

Question 9

Two ideal oscillators have the same amplitude and angular frequency, but one has phase constant 0 and the other π. How are their motions related?

Accepted Answer

They are exactly out of phase by half a cycle

Answer

They are in phase

Answer

They differ by a quarter cycle

Answer

They have different periods

Question 10

For a simple pendulum at small angles, which factor does NOT affect the period?

Accepted Answer

Mass of the bob

Answer

Local gravitational acceleration

Answer

Pendulum length

Answer

Value of π in the formula

Question 11

At what displacement in ideal SHM are kinetic and potential energies equal in magnitude?

Accepted Answer

x = ±A/√2

Answer

x = 0

Answer

x = ±A

Answer

x = ±A/2

Question 12

Which unit is the SI unit of angular frequency in SHM?

Accepted Answer

radian per second

Answer

hertz

Answer

radian

Answer

cycle per second squared

Question 13

A mass on a spring oscillates with angular frequency ω. What is the maximum speed?

Accepted Answer

Aω

Answer

A/ω

Answer

ω/A

Answer

Aω²

Question 14

Which physical situation is best approximated by simple harmonic motion only for small displacements?

Accepted Answer

A simple pendulum

Answer

An undamped LC circuit

Answer

A block on an ideal Hooke's law spring

Answer

A torsion oscillator with linear torque

Question 15

If the spring constant of an ideal oscillator is increased by a factor of 9 while the mass stays the same, the period becomes:

Accepted Answer

One third as large

Answer

Three times larger

Answer

Nine times larger

Answer

Unchanged

Question 16

Which quantity remains constant throughout ideal simple harmonic motion?

Accepted Answer

Mechanical energy

Answer

Displacement

Answer

Velocity

Answer

Restoring force

Question 17

For ideal SHM, which differential equation matches the motion?

Accepted Answer

d²x/dt² = -ω²x

Answer

d²x/dt² = +ω²x

Answer

dx/dt = -ω²x

Answer

d²x/dt² = -ωx

Question 18

What is the phase difference between displacement and acceleration in ideal SHM?

Accepted Answer

π

Answer

0

Answer

π/2

Answer

3π/2

Question 19

Which change would make a real oscillator depart most clearly from ideal SHM behavior?

Accepted Answer

Introducing significant damping

Answer

Measuring time more precisely

Answer

Choosing a smaller unit of length

Answer

Starting at equilibrium

Question 20

A body executing SHM takes 0.20 s to move from equilibrium to one extreme. What is its period?

Accepted Answer

0.80 s

Answer

0.20 s

Answer

0.40 s

Answer

1.60 s

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