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Question
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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