SHM

SHM 1

Simple Harmonic Motion

Fill in the Blanks

Harmonic motion is motion that _______ itself.

e.g.

clock hand

Simple harmonic motion is a special case.

An example is a mass oscillating horizontally along a friction-less surface while attached to a spring.

The key distinction is that for a body undergoing SHM the acceleration is proportional to the ____________ and it is always directed towards the equilibrium position.

Fill in the Blanks

Now of course an acceleration requires a force. This is provided by the spring. The restoring force is proportional to the dispacement

The restoring force is always

towards the equilibrium posistion

Multiple Choice

As a mass attached to the end of a spring moves with SHM, the point where kinetic energy is zero is

• at maximum displacement from the equilibrium position

• at the equilibrium position

• at the midpoint between the maximum displacement and the equilibrium position

Multiple Choice

As a mass attached to the end of a spring moves with SHM, the point where kinetic energy is maximum is

• at maximum displacement from the equilibrium position

• at the equilibrium position

• at the midpoint between the maximum displacement and the equilibrium position

Multiple Choice

As a mass attached to the end of a spring moves with SHM, the point where elastic potential energy is minimum is

• at maximum displacement from the equilibrium position

• at the equilibrium position

• at the midpoint between the maximum displacement and the equilibrium position

Multiple Choice

As a mass attached to the end of a spring moves with SHM, the point where elastic potential energy is maximum is

• at maximum displacement from the equilibrium position

• at the equilibrium position

• at the midpoint between the maximum displacement and the equilibrium position

Multiple Select

Select all true statements about SHM

• $a=-\omega^2x$

• $a\propto-x$

• $a=-x$

• The restoring force always acts towards the equilibrium position

Multiple Select

Select all true statements

• acceleration is directly proportional to negative displacement

• the frequency of oscillation can be calculated from the gradient of this graph

• ω²A should be the label for maximum acceleration

• gradient = -ω

Multiple Choice

What provides the restoring force for the tuning fork?

• force of gravity

• elastic force of metal

• magnetic force

Pattern of SHM

The pattern traced out by a body undergoing SHM can be mapped using a reference circle

Fill in the Blanks

As the mass on the spring bounces up and down the green phasor point completes one period of rotation about the circle.

Notice when the mass reaches the top velocity is ____.

When the mass is half way up or down velocity is _______.

Fill in the Blanks

This image shows the vertical displacement of the spring through time. Notice the shape is sinusoidal.

The reference circle maps out the vertical displacement with the red dot and the phasor with the black dot.

As the spring completes one oscillation the

completes on full circle.

Multiple Choice

We can generate an equation for the spring's displacement from the reference circle using simple trigonometry. At any time t, the equation for displacemnt y, is:

• $y=A\sin\omega t$

• $y=A\sin t$

• $y=\omega t$

• $y=A\omega t$