Physics 9702 · AS & A Level · Simple harmonic oscillations
Simple harmonic oscillations — practice question
A piston inside a car engine cylinder undergoes simple harmonic motion as it travels within the cylinder. It moves from the highest position in the cylinder to the lowest position, as shown in Fig. 3.1. The separation between the two positions in Fig. 3.1 is $9.8\ \text{cm}$. The piston has a mass of $640\ \text{g}$. At a certain engine speed, the piston makes $2700$ oscillations in $1.0$ minute.
(a(i))[1]
For the piston’s oscillations in the cylinder, determine the amplitude.
(a(ii))[1]
For the piston’s oscillations in the cylinder, determine the frequency.
(a(iii))[2]
For the piston’s oscillations in the cylinder, determine the maximum speed.
(a(iv))[2]
Find the speed when the piston’s top is $2.3\ \text{cm}$ below its maximum height.
(b)[3]
The piston’s acceleration changes. Determine the resultant force on the piston that produces its maximum acceleration.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The amplitude is $4.9\,\text{cm}$” …