Topic 3.1: Simple Harmonic Motion Questions

An air molecule oscillates with simple harmonic motion of frequency 256 Hz.

Calculate the time it takes to move from the equilibrium position to the point of maximum displacement.

An energy-against-displacement graph for an oscillator shows the potential energy as an upward parabola reaching 0.18 J at each end (the amplitude), and the kinetic energy as a downward parabola.

Outline what the graph tells you about the total energy of the oscillation, and state the maximum kinetic energy of the oscillator.

A glider on an air track oscillates with simple harmonic motion between two springs.

State the position in the oscillation at which

A simple pendulum of length 0.90 m swings with small oscillations on Earth, where g = 9.8 m s⁻².

An oscillator completes one full cycle every 0.50 s.

An object performs simple harmonic motion.

State, in terms of T, the time it takes to travel from one extreme of its motion to the other extreme.

A 0.40 kg block oscillates on a horizontal spring of spring constant 250 N m⁻¹.

Calculate the natural frequency of the oscillation.

State the two conditions that the acceleration of an object must satisfy for the object to be undergoing simple harmonic motion.

Displacement-time graphs are drawn for the displacement x, the velocity v and the acceleration a of an oscillator in simple harmonic motion.

Identify, on these graphs, the point in the cycle where the velocity has its greatest magnitude.

The graph shows how the displacement d of a particle varies with time t.

The time t is in milliseconds (ms) and the displacement d is in millimetres (mm).

Determine the frequency and the amplitude of the oscillation.

[Diagram: x-axis from 0 to 4 label t, y-axis from -5 to 5 label d, polyline: (0,0)-(0.25,2.8)-(0.5,4)-(0.75,2.8)-(1,0)-(1.25,-2.8)-(1.5,-4)-(1.75,-2.8)-(2,0)-(2.25,2.8)-(2.5,4)-(2.75,2.8)-(3,0)-(3.25,-2.8)-(3.5,-4)-(3.75,-2.8)-(4,0)]

A small block of wood floats at rest on the surface of a tank of water.

It is pushed down a short distance and released, after which it bobs up and down.

Outline why the block undergoes simple harmonic motion, and state what the minus sign in a = -ω²x represents.

A simple pendulum oscillates with angular frequency ω.

Its bob's mass is then doubled and its length is reduced to one quarter of the original.

Determine the new angular frequency in terms of ω.

A student claims that any object moving back and forth about a fixed point must be undergoing simple harmonic motion.

Identify why this claim is not necessarily correct.

A child's playground swing is given a single push and then left alone.

Because of air resistance and friction at the pivot, it undergoes lightly damped oscillation.

Which statement correctly describes the motion of the swing as it gradually comes to rest?

The acceleration of a 0.25 kg block oscillating on a horizontal spring is found to be proportional to its displacement, with the data fitting a = -49x (a in m s⁻², x in m).

Determine the angular frequency of the oscillation and the magnitude of the net force on the block when its displacement is 3.0 cm.

A clockmaker builds a pendulum of length 0.25 m for a timing device (g = 9.8 m s⁻²).

Calculate the frequency of the pendulum, and explain why the period would not change if a slightly heavier bob were fitted.

A mass on a single spring oscillates with period T.

An identical second spring is connected in parallel with the first so that the two together provide a combined spring constant of 2k.

State the new period of oscillation in terms of T.

On Earth a simple pendulum used in a science demonstration has a period of 1.8 s.

The whole apparatus is flown to a research station on a distant moon where the gravitational field strength is one quarter of its value on Earth.

There the experimenter also replaces the bob with one of three times the mass, while keeping the string length unchanged.

What is the period of the pendulum on the moon?

A loudspeaker cone moves with simple harmonic motion.

A simple pendulum swings with small-amplitude oscillations of angular frequency ω₀.

The pendulum is then rebuilt so that its string is 9 times as long as before and its bob has 3 times the original mass.

What is the new angular frequency of the pendulum?