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A Particle Performing Linear S.H.M. Has a Period of 6.28 Seconds and a Pathlength of 20 cm. What is the Velocity When Its Displacement is 6 cm from Mean Position? - Physics

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Sum

A particle performing linear S.H.M. has a period of 6.28 seconds and a pathlength of 20 cm. What is the velocity when its displacement is 6 cm from mean position?

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Solution

Given:

T = 6.28s

Pathlength 20cm

∴ a =10 cm = 10×10-2m

x = 6 ×10-2m

To find:

Velocity, v = ?

Solution:

`omega = (2pi)/t`

`omega = (2xx3.14)/6.28`

`omega = 1"rad/s"`

`"V" = "W" sqrt ("A"^2 - "x"^2)`

`= 1 sqrt ((10^2 - 6^2) xx 10 ^-4)`

`v = sqrt((100-36)xx10^-4)`

`v = 1 xx 8 xx 10^-2`

`v=8 xx 10^-2 "m/s"`

Concept: Differential Equation of Linear S.H.M.
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