Question

The velocities of a particle performing linear S.H.M are 0.13 m/s and 0.12 m/s, when it is at 0.12 m and 0.13 m from the mean position respectively. If the body starts from mean position, the equation of motion is ____________.

Options

• x = sint

• `"x" = "sin" sqrt313  "t"`

• `"x" = sqrt313  "sin" sqrt313  "t"`

• `"x" = sqrt313  "cos" sqrt313  "t"`

Answer 1

The velocities of a particle performing linear S.H.M are 0.13 m/s and 0.12 m/s, when it is at 0.12 m and 0.13 m from the mean position respectively. If the body starts from mean position, the equation of motion is `"x" = "sin" sqrt313  "t"`.

Explanation:

Using,

`"y" = omega sqrt ("A"^2 - "X"^2)  "we get,"`

`169 = omega^2 "A"^2 - omega^2 xx 144 and`

`144 = omega^2 "A"^2 - omega^2 xx 169;`

`therefore 169 - 144 = 169  omega^2 - 144  omega^2`

`therefore 25 = 25  omega^2;`

`therefore omega^2 = 1;`

`therefore 169 = omega^2 ("A"^2 - 144);`

`therefore "A"^2 = 313;`

`therefore "A" = sqrt313`

`therefore "x" = sqrt313  "sin t"`