Igcse Model Questions Vol1 2018 Physics Question 4

A spring is fixed at one end and a dynamics cart is attached to the free end. The cart is allowed to hang vertically when masses are placed on it. The following data are recorded. **Static method** – masses added (kg) and the resulting extension of the spring (cm): | Mass (kg) | Extension (cm) | |-----------|----------------| | 0.10 | 2.5 | | 0.20 | 5.0 | | 0.30 | 7.5 | | 0.40 | 10.0 | **Dynamic method** – the cart with each mass is set into simple harmonic motion and the period of 10 oscillations is measured. The period (s) for each mass is: | Mass (kg) | Period for 10 oscillations (s) | |-----------|--------------------------------| | 0.10 | 3.20 | | 0.20 | 4.50 | | 0.30 | 5.50 | | 0.40 | 6.30 | Using the data, determine the spring constant k by both methods and comment on the agreement. (Assume g = 9.8 m s⁻² and use T = 2π√(m/k) for the dynamic method.)