Topic 3.1: Simple Harmonic Motion Questions

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

Calculate (a) its period and (b) its frequency.

An oscillator completes one full cycle every 0.50 s.

Determine (a) its angular frequency and (b) its frequency, and state the relationship that links the two.

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.

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) the kinetic energy is a maximum, and (b) the potential energy is a maximum.

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.

Describe how the velocity of an object in simple harmonic motion changes as it moves from the equilibrium position out to its maximum displacement.

A pendulum bob swings with simple harmonic motion.

At one instant its kinetic energy is 0.030 J and its potential energy is 0.090 J.

Determine the total energy of the oscillation, the kinetic energy of the bob as it passes through the lowest point, and explain why these are equal.

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.)

A student measures the kinetic energy of an oscillating mass at several points in its swing and finds that the value is different at each point.

Explain why, despite this, the total energy of the oscillation is the same at every point, assuming there is no friction.

An oscillator on a fixed spring has its amplitude doubled while the spring and mass are unchanged.

Deduce the factor by which (a) the total energy and (b) the maximum speed of the oscillator change.

A particle in simple harmonic motion has a period of 0.40 s.

At time t = 0 it is at its maximum displacement.

Determine the first time after t = 0 at which the particle's acceleration is zero.

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 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 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 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.

A trolley attached to a spring oscillates with simple harmonic motion.

Its period is 0.60 s and it is released from its maximum displacement.

Determine the time it first takes to reach the equilibrium position, and state the velocity and acceleration of the trolley at that instant (qualitatively).