The periodic time of a linear harmonic oscillator is $2 π$ seconds, with maximum displacement of $1 c m$ , if the particle starts from extreme position, find displacement of the particle after $\frac{π}{3}$ seconds.

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Solution

Displacement $X = A cos ω t$
Substitute $A = 1$ cm, $T = 2 π$ secs, $t = \frac{π}{3}$ secs
hence, $X = 1 \times cos \frac{2 π t}{T}$
$= 1 \times cos \frac{2 π \times \frac{π}{3}}{2 π}$
$= cos \frac{π}{3}$
$= 0.5$ cm

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The periodic time of a linear harmonic oscillator is 2π seconds, with maximum displacement of 1cm, if the particle starts from extreme position, find displacement of the particle after π3 seconds.

DisplacementX=AcosωtSubstitute A=1cm,T=2πsecs, t=π3secshence, X=1×cos2πtT=1×cos2π×π32π=cosπ3=0.5cm

The periodic time of a linear harmonic oscillator is $2 π$ seconds, with maximum displacement of $1 c m$ , if the particle starts from extreme position, find displacement of the particle after $\frac{π}{3}$ seconds.

Displacement $X = A cos ω t$
Substitute $A = 1$ cm, $T = 2 π$ secs, $t = \frac{π}{3}$ secs
hence, $X = 1 \times cos \frac{2 π t}{T}$
$= 1 \times cos \frac{2 π \times \frac{π}{3}}{2 π}$
$= cos \frac{π}{3}$
$= 0.5$ cm