Question

The maximum velocity and maximum acceleration of a particle executing .H.M. are 1m/ and 3.14m/s2 respectively. The frequency of oscillation for this particle is……

(A) 0.5s–1

(B) 3.14s–1

(C) 0.25s–1

(D) 2s–1

Answer 1

The correct option (A) 0.5s–1

Explanation:

Vmax = 1m/*

amax = 3.14m/s2

x = Asinωt

V = (dx/dt) = Aωcosωt

∴ at cosωt = 1, Vmax occurs

& Vmax = Aω

also amax = Aω2

∴ {Vmax/amax} = (1/ω)

∴ {1/(3.14)} = (1/ω)

ω = 3.14

i.e. 2πf = 3.14

f = {(3.14)/2π}

f = (1/2)

f = 0.5s–1