Topic 3.1: Simple Harmonic Motion Questions

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

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.

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

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.

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.

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.

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

State the position in the oscillation at which

An oscillator completes one full cycle every 0.50 s.

A small block of mass 0.40 kg is attached to a single light spring of spring constant k and oscillates horizontally on a frictionless bench with period T. A second, identical spring (also of spring constant k) is then connected so that the two springs act in parallel on the same block, doubling the effective spring constant. The block is set oscillating again with the same mass.

What is the new period of oscillation?

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 loudspeaker cone moves with simple harmonic motion.

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 student measures the period of a mass oscillating on a spring of spring constant 120 N m⁻¹ to be 0.80 s.

Show that the oscillating mass is about 1.9 kg.

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 pendulum bob oscillates with simple harmonic motion and a total energy of 0.20 J.

At the instant the bob is at half of its amplitude (x = A/2), determine its potential energy and its kinetic energy.

(For SHM the potential energy at displacement x is a fraction (x/A)² of the total energy.)

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 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 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?