The defining equation of simple harmonic motion is $a = -\omega^2 x$. State what the minus $(-)$ sign indicates in the equation.
A trolley stands on a bench. Two identical stretched springs are connected to the trolley as shown in Fig. 4.1. The other end of each spring is fixed to a support. The unstretched length of each spring is $12.0\,\text{cm}$. The spring constant of each spring is $8.0\,\text{N m}^{-1}$. When the trolley is in equilibrium the length of each spring is $18.0\,\text{cm}$. The trolley is displaced $4.8\,\text{cm}$ to one side and then released. Assume that resistive forces on the trolley are negligible. Show that the resultant force on the trolley at the instant of release is $0.77\,\text{N}$.
A trolley stands on a bench. Two identical stretched springs are connected to the trolley as shown in Fig. 4.1. The unstretched length of each spring is $12.0\,\text{cm}$. The spring constant of each spring is $8.0\,\text{N m}^{-1}$. When the trolley is in equilibrium the length of each spring is $18.0\,\text{cm}$. The trolley is displaced $4.8\,\text{cm}$ to one side and then released. Assume that resistive forces on the trolley are negligible.
The mass of the trolley is $250\,\text{g}$. Calculate the maximum acceleration $a$ of the trolley.
Use your answer in (ii) to find the period $T$ of the next oscillation.
The experiment is repeated with an initial displacement of the trolley of $2.4\,\text{cm}$. State and explain the effect, if any, this change has on the period of the oscillation of the trolley.