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A Body of Mass 1 Kg is Made to Oscillate on a Spring of Force Constant 16 N/M. Calculate: Angular Frequency Frequency of Vibration. - Physics

A body of mass 1 kg is made to oscillate on a spring of force constant 16 N/m. Calculate:

a) Angular frequency

b) frequency of vibration.

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Solution

m = 1 kg, K = 16 N/m

ω = ?, n = ?

We have, for S.H.M.

ω = `sqrt(K/M)`

= `sqrt(16/1)`

∴ ω = 4 rad/s

Also, ω = 2πn

∴ n = `ω/(2pi)`

=  `4/(2pi) = 2/pi Hz`

∴ n = `2/3.14 = [log(2) - log(3.14)]`

= [0.3010 − 0.4969]

= antilog [1.8041]

= 0.6369

= 0.6369 Hz

The angular frequency of the body is 4 rad/s and the frequency of vibration is 0.6369 Hz.

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