B.5) Current and circuits

You can also download the questions here (ill link it later).

C.1) Simple harmonic motion

Simple harmonic motion refers to periodic motion through an equilibrium where the restoring force is proportional to the displacement from the equilibrium. Therefore, the acceleration is pointed towards the equilibrium and is proportional to the distance from the point. The acceleration at the equilibrium is therefore zero.

On a spring, this is represented as:

\( F = -kx \)

F - restoring force
k - spring constant
x - displacement

The negative sign represents the force acting opposite to the direction of the displacement.

Real examples of SMH

• Mass-spring systems
• Simple pendulums
• Vibrating strings and air columns in musical instruments
• Molecular vibrations

First two formulas

The amount of time taken for an oscillation to complete is period (s).

Frequency = Number of cycles / second. It is measured in hertz (Hz).

The amount of oscillations in one period is 1:

f = \(\frac{1}{T} \)

Which means its inversely related, it can also be rearranged to \( T = \frac{1}{f} \)


Angular frequency \((\omega)\) is the angle the oscillation covers every second.

Therefore \( (\omega) = \frac{\text{radians}}{T} \), where \( T \) is the period (s).

In one complete period an oscillation completes one cycle which is \( 2\pi \) radians. This is the same in unit circle in math. Therefore the rate that an oscillation completes a cycle is:

\( \omega = \frac{2\pi}{T} \)

It's rearranged to make your life more difficult.

This next formula has to do with newtons second law \(F = ma\)

As previously mentioned, force is also \(-kx\) in SMH, \(ma = -kx\). This can rearrange to \(a = \frac{-k}{m} x \)

Angular frequency is also \( \omega = \sqrt{\frac{k}{m}} \), which you dont need to know why.
This means that \( a = -\omega^2 x \), by using substitution. If you graph this, you get:

The gradient of this graph is \(-\omega^2\), and is negative because acceleration and displacement are in opposite directions

Last two formulas - This section will be updated

In a pendulum, time period is independent from mass, the heavier object will not make an decrease time period (assuming no air resistance).

This is from \(F=ma\). The restoring force is gravity, which has a force of \(F=mg\)
mg = ma, so the mass cancels out.

The explanation on how this was calculated is a bit long, and is not very necessary to know. It involves three previously known formulas and an approximation method using small angles.
Explanation (scroll to: Deriving the time period of a pendulum)

\( T = 2\pi \sqrt{\frac{l}{g}} \)

In the next formula the time period is dependent on mass, since this is analysing a mass-spring system. This formula is once again composed of the previously known ones substituted into one another.
Explanation (scroll to: Mass-spring system)

\( T = 2\pi \sqrt{\frac{m}{k}} \)

Energy transfers

In a pendulum, at the top it is only GPE, at the equilibrium it's just kinetic energy.

In a horizontal spring, at the sides it is elastic potential energy and in equilibrium kinetic energy.

In a vertical spring, at the top it is GPE and elastic potential energy at the top and only elastic energy at the bottom.

C.2) Wave model