A data probe attached to a glider on a friction-free air track records the glider’s…

PHYSICS · Multi-part · CBSE · Physics · Oscillations · Oscillations

Problem

A data probe attached to a glider on a friction-free air track records the glider’s velocity as a function of time and reports the analytical expression

v(t)=1.20\cos\!\bigl(\pi t +0.30\bigr)\;\text{m}\,\text{s}^{-1}

for

t

in seconds. Assume the motion arises from an ideal linear restoring force and that no damping is present. (a) Determine the numerical value of the period

T

of the glider’s motion. (b) Compute the earliest time

t>0

at which the glider’s displacement is zero and the glider is moving in the positive direction. (c) The probe time-stamps an event at

t=1.0\text{ s}

. Determine the next later time at which the glider’s acceleration is zero. (d) Starting from the velocity expression, derive (without invoking any external relationships) a simplified expression for the displacement

x(t)

that is consistent with the given velocity function. Use your expression to verify one of your answers from parts (b) or (c).

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