Two light, ideal springs are suspended vertically in series from a fixed support.…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
Two light, ideal springs are suspended vertically in series from a fixed support. Spring H, attached to the support, has a force constant of 250 N/m. Spring I is attached below Spring H and has a force constant of 150 N/m. A 2.0 kg mass is hung from the lower end of Spring I and allowed to come to rest.
(a) Determine the individual extensions of Spring H and Spring I when the mass is in static equilibrium. Express each extension symbolically in terms of m, g, kH, and kI before substituting numerical values.
(b) Show that the total extension of the two-spring system equals the extension that would result if a single spring of appropriate force constant were used. State the value of that single spring constant.
(c) Derive an expression for the period of small vertical oscillations of the mass about its equilibrium position in terms of m, kH, and kI.
(d) Calculate the numerical value of the period using g=9.8m/s2 and the given spring constants.