9.1 Simple Harmonic Motion

Which graph correctly shows how the kinetic energy of an oscillator varies as a function of time through one complete oscillation?

Which equation correctly shows the kinetic energy-displacement relation for simple harmonic motion?

The defining equation of SHM describes the relationship between acceleration, a, angular frequency, ω, and displacement, x, from the equilibrium position:

Which value correctly shows the resulting acceleration if the angular frequency was doubled?

The graph shows the displacement over time of a simple pendulum oscillating in simple harmonic motion. 

What is the potential energy of the pendulum at points X, Y and Z?

A spring loaded with mass m oscillates with simple harmonic motion. The amplitude of the motion is A and the spring has total energy E.

What is the total energy of the spring when both the mass and the amplitude are doubled?

A simple pendulum undergoes simple harmonic motion. The kinetic energy of the pendulum is at a maximum at the equilibrium position.

How many times during one oscillation is the kinetic energy of the pendulum equal to its gravitational potential energy?

A mass with mass, m, is attached to a spring with a spring constant, k, and oscillates in simple harmonic motion with a period, T. 

A new spring is introduced with a spring constant of 4k. How does this affect the period of the oscillation?

A small ball is attached to a thread of length l, and set to oscillate isochronously.

If the length of the thread is reduced by 10%, what effect will this have on the period, T, of the oscillation?

A particle oscillates in simple harmonic motion. The particle's displacement over time is shown in the following graph.

Which graphs are the correct velocity-time and acceleration-time graphs for this particle?