Two identical carts of mass are attached to separate

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

Problem

Two identical carts of mass

m

are attached to separate, identical ideal springs fixed to a rigid wall on a frictionless horizontal track. Cart A is pulled to

x=+0.08\,\text{m}

and released from rest, while Cart B is pulled to

x=+0.16\,\text{m}

and released from rest. A motion sensor records each cart’s position as a function of time. The resulting displacement–time graphs are sinusoidal with the following features: • Cart A: successive maxima occur at

t=0.00\,\text{s},\;0.64\,\text{s},\;1.28\,\text{s},\ldots

• Cart B: successive maxima occur at

t=0.00\,\text{s},\;0.64\,\text{s},\;1.28\,\text{s},\ldots

(a) Using the information above, determine the experimental period of oscillation for each cart. (b) Compare the amplitudes and periods of the two carts, citing specific numerical values from the graphs. (c) Provide a qualitative explanation for why the periods are identical even though the amplitudes differ. (d) The sensor also records velocity. Explain how and why the maximum speed of Cart B compares with that of Cart A.

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