This diagram shows the piston of a small car engine that oscillates in the cylinder with a motion that approximates simple harmonic motion at $4200$ revs per minute $\left(1 rev=1cycle\right).$ The mass of the piston is $0.24kg$

The amplitude of the oscillation is $12.5cm$. Calculate the forces required on the piston to produce the maximum acceleration.

This diagram shows a turntable with a rod attached to it a distance $15 \mathrm{cm}$ From the centre. The turntable is illuminated from the side so that a shadow is cast on a screen.

A simple pendulum is placed behind the turntable and is set oscillating so that it has an amplitude equal to the distance of the rod from the centre of the turntable. The speed of rotation of the turntable is adjusted. When it is rotating at $1.5$ Revolutions per second the shadow of the pendulum and the rod are found to move back and forth across the screen exactly in phase. Explain what is meant by the term in phase.

This diagram shows a turntable with a rod attached to it a distance $15 \mathrm{cm}$ From the centre. The turntable is illuminated from the side so that a shadow is cast on a screen.

A simple pendulum is placed behind the turntable and is set oscillating so that it has an amplitude equal to the distance of the rod from the centre of the turntable. The speed of rotation of the turntable is adjusted. When it is rotating at $1.5$ Revolutions per second the shadow of the pendulum and the rod are found to move back and forth across the screen exactly in phase. Explain what is meant by the term in phase. Write down an equation to describe the displacement $x$ of the pendulum from its equilibrium position and the angular frequency of the oscillation of the pendulum.

This diagram shows a turntable with a rod attached to it a distance $15 \mathrm{cm}$ From the centre. The turntable is illuminated from the side so that a shadow is cast on a screen.

A simple pendulum is placed behind the turntable and is set oscillating so that it has an amplitude equal to the distance of the rod from the centre of the turntable. The speed of rotation of the turntable is adjusted. When it is rotating at $1.5$ Revolutions per second the shadow of the pendulum and the rod are found to move back and forth across the screen exactly in phase. The turntable rotates through $60°$ From the position of maximum displacement shown in the diagram. Calculate the displacement (from its equilibrium position) of the pendulum at this point.

This diagram shows a turntable with a rod attached to it a distance $15 \mathrm{cm}$ From the centre. The turntable is illuminated from the side so that a shadow is cast on a screen.

A simple pendulum is placed behind the turntable and is set oscillating so that it has an amplitude equal to the distance of the rod from the centre of the turntable. The speed of rotation of the turntable is adjusted. When it is rotating at $1.5$ Revolutions per second the shadow of the pendulum and the rod are found to move back and forth across the screen exactly in phase. The turntable rotates through $60°$ From the position of maximum displacement shown in the diagram. Calculate its speed at this point.

This diagram shows a turntable with a rod attached to it a distance $15 \mathrm{cm}$ From the centre. The turntable is illuminated from the side so that a shadow is cast on a screen.

A simple pendulum is placed behind the turntable and is set oscillating so that it has an amplitude equal to the distance of the rod from the centre of the turntable.

The speed of rotation of the turntable is adjusted. When it is rotating at $1.5$ Revolutions per second the shadow of the pendulum and the rod are found to move back and forth across the screen exactly in phase.

The turntable rotates through $60°$ From the position of maximum displacement shown in the diagram.Through what further angle must the turntable rotate before it has this speed again?

When a cricket ball hits a cricket bat at high speed it can cause a standing wave to form on the bat. In one such example, the handle of the bat moved with a frequency of 60Hz with an amplitude of 2.8mm. The vibrational movement of the bat handle can be modelled on simple harmonic motion. State the conditions for simple harmonic motion.

When a cricket ball hits a cricket bat at high speed it can cause a standing wave to form on the bat. In one such example, the handle of the bat moved with a frequency of 60Hz with an amplitude of 2.8mm. The vibrational movement of the bat handle can be modelled on simple harmonic motion. Calculate the maximum acceleration of the bat handle.

When a cricket ball hits a cricket bat at high speed it can cause a standing wave to form on the bat. In one such example, the handle of the bat moved with a frequency of 60Hz with an amplitude of 2.8mm. The vibrational movement of the bat handle can be modelled on simple harmonic motion. Given that the part of the bat handle held by the cricketer has a mass of $0.48 kg$, calculate the maximum force produced on his hands.