A horizontal spring–mass system oscillates with amplitude and time period

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Oscillations · Oscillations

Problem

A horizontal spring–mass system oscillates with amplitude

10\,\text{cm}

and time period

2.0\,\text{s}

. The particle is released from the mean position at

t=0

. (i) Calculate the time taken by the particle to reach a displacement of

6.0\,\text{cm}

for the first time. (ii) Determine the total duration, within one complete oscillation, for which the magnitude of displacement satisfies

|x|<6.0\,\text{cm}

. (iii) What percentage of the time period does the duration found in part (ii) represent?