Physics

Physics

Problem

A body executes simple harmonic motion with amplitude 4 cm4\,\text{cm} and time period 0.50 s0.50\,\text{s}. It passes through the mean position at t=0t=0. Find its displacement at t=0.125 st=0.125\,\text{s}. a) −0.04 m-0.04\,\text{m} b) +0.028 m+0.028\,\text{m} c) +0.04 m+0.04\,\text{m} d) +0.015 m+0.015\,\text{m}
Intuitive explanation

In simple harmonic motion, the displacement follows a sinusoidal pattern determined by amplitude and period. Since the body passes through the mean position (zero displacement) at t=0t=0, you know the motion starts with maximum velocity—this tells you whether to use a sine or cosine function. Once you write the correct equation of motion, substitute the given time to find where the body has traveled.

Intuitive explanation

In simple harmonic motion, the displacement follows a sinusoidal pattern determined by amplitude and period. Since the body passes through the mean position (zero displacement) at t=0t=0, you know the motion starts with maximum velocity—this tells you whether to use a sine or cosine function. Once you write the correct equation of motion, substitute the given time to find where the body has traveled.

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