Two spring–mass systems, I and II

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

Two spring–mass systems, I and II, oscillate independently on smooth horizontal surfaces. The following data are provided: • System I: mass m1=0.40 kgm_1 = 0.40\,\text{kg}, spring constant k1=64 N m−1k_1 = 64\,\text{N\,m}^{-1}, amplitude A1=0.05 mA_1 = 0.05\,\text{m} • System II: mass m2=0.20 kgm_2 = 0.20\,\text{kg}, spring constant k2=36 N m−1k_2 = 36\,\text{N\,m}^{-1}, amplitude A2=0.04 mA_2 = 0.04\,\text{m} Answer the following: (i) Derive an expression for the ratio vmax,Ivmax,II\dfrac{v_{\text{max},I}}{v_{\text{max},II}} of the maximum speeds of the two systems in terms of m1,m2,k1,k2,A1,m_1, m_2, k_1, k_2, A_1, and A2A_2. (ii) Using the given numerical data, evaluate this ratio. (iii) State which system attains the larger maximum speed and justify your answer with reference to your calculation.

Related theory

Browse the problem library