Home » Maths for Planet Earth » A New Renewable

A New Renewable


A scientist wishes to develop a new way of generating renewable energy.

They decide to use a large magnet on a large spring, oscillating through a coil of wire, generating a current that could then charge a battery, which in turn would store the energy released from the system.

The system is set into motion with a winch system that can be used to set the spring. The following equation can then be used to describe the oscillations, in metres, t minutes after it has been set into motion:

\[A = 10e^{- 0.05t}\cos{10t}\]

a) On a plot of A against t, show that the t values of the
turning points satisfy the equation \(\tan{10t} = – \frac{1}{200}\)

[4 marks]

The battery can only be charged when the amplitude of the oscillations of the spring are greater than 1m. The amplitudes, A, of the oscillations are found at the turning points of the curve.

b) Give the t value of the last turning point where |A|≥1m, and the battery can no longer be charged.

[4 marks]

Start exploring

Latest from blog

More Maths for Planet Earth

Climate change can lead to species extinction through changing habitats rapidly, not leaving the species time to adapt. Warming at the moment is at
A Level
A country wishes to achieve net-zero CO2 emissions in 50 years.  At the start of the program their emissions are 800MtCO2 year-1.  They decide
Global warming will affect the world’s coral reefs. In a world heated by a global warming of 2°C, we will lose 99% of coral
A Level
A country decides to begin a reforestation program, starting in 2020, gradually increasing the number of trees planted per year by the same amount