Two ideal springs are connected to a rigid wall on one side and to a single block on…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
Two ideal springs are connected to a rigid wall on one side and to a single 0.75kg block on the other side so that the block can slide horizontally on a frictionless surface. The springs, which remain aligned along the same axis, have spring constants k1=60N/m and k2=90N/m.
(a) The springs are first arranged in parallel, each attached directly between the wall and the block. Determine the single spring constant that is equivalent to this parallel arrangement.
(b) Using your result from part (a), calculate the period of small oscillations of the block for the parallel arrangement.
(c) The springs are now reconfigured in series, with spring k1 attached to the wall, spring k2 attached between k1 and the block, and no other springs present. Determine the single spring constant that is equivalent to this series arrangement, and calculate the corresponding oscillation period of the block.
(d) Compare the two periods obtained in parts (b) and (c). Explain physically why arranging the same two springs in series versus parallel leads to different oscillation periods for the same block.