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in Physics by (64.7k points)

A simple harmonic oscillation is represented by the equation:

y = 0.40 sin (440 t + 0.61),

where y and t are in metre and second respectively. What are the values of (i) amplitude, (ii) angular frequency,. (iii) frequency of oscillations, (iv) time period of oscillations and (v) initial phase?

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The given equation is

y = 0.40 sin (440 t + 0.61)

Comparing it with the equation of S.H.M

y = a sin (ωt + ϕ0)

We have (i) amplitude, a = 0.40 m

(ii) Angular frequency, ω = 440 Hz

(iii) Frequency of oscillations

v = ω/2π = {440}/{2 x 22/7} = 70 Hz

(iv) Time period of oscillations,

T = 1/v = 1/70 = 0.0143 s.

(v) Initial phase angle, ϕ = 0.61 rad

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