Two identical masses are suspended from different springs, X and Y
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
Two identical 0.200kg masses are suspended from different springs, X and Y, and set into small-amplitude vertical oscillations. A motion sensor records the periods of the oscillations as
• spring X: 0.60s
• spring Y: 0.80s
(a) Derive an expression for the stiffness constant of a spring in terms of the oscillation period T and the attached mass m.
(b) Determine the numerical value of the stiffness constant for each spring, including units.
(c) Identify which spring is stiffer and calculate the factor by which its stiffness differs from that of the other spring.
(d) If the amplitude of oscillation for spring X is doubled while the mass remains the same, qualitatively discuss how (i) the period and (ii) the maximum restoring force change, supporting each answer with appropriate reasoning.