The velocity of a particle executing simple harmonic motion is 16cm/s at a distance of 8cm from the mean position and 8cm/s at a distance of 12cm from the mean position. Calculate the amplitude of the motion.

Given,

For 1st Condition,
Velocity v=16cm/s
Displacement y=8cm
v=ωr2y2
16=ωr264 .......... (i)

Amplitude of the motion r=?
For 2nd Condition,
Velocity v=8cm/s
Displacement y=12cm
v=ωr2y2
8=ωr2144 .......... (ii)

From equation (i) and (ii), we get

168=r2y2r264
or, 4= r264r2144
or, 4r21444=r264
or, 3r2=512
or, r2=170.66cm
or, r=13.06cm

∴The amplitude of the motion is 13.06cm

Return to Main Menu

No comments:

Post a Comment