A simple harmonic oscillation is represented by the equation:y = 0.40

1.	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?
Answer» 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

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?

Answer»

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