Question

A particle executing simple harmonic motion has an amplitude of 1m and a time

period of 2 seconds. At t=0, net force on the particle is 0. The equation of

displacement of the particle is​

Answer 1

amplitude , A = 1m

time period , T = 2 second.

so, frequency of particle is , f = 1/T = 0.5 Hz

now angular frequency, w = 2πf = 2π × 0.5 = π m/s

Let equation of particle executing simple harmonic motion, $y=Asin(\omega t+\phi)$

or, y = (1m)sin(πt + Ф) ......(1)

a/c to question,

net force on the particle at (t = 0) is 0.

means, acceleration of particle at t = 0 is zero.

we say, d²y/dt² = 0 at t = 0s

now given equation (1) is being differentiated twice .

dy²/dt² = -π²(1m)sin(πt + Ф)

putting t = 0,

0 = -π²sin(π × 0 + Ф) => sinФ = 0

then, Ф = 0

so, equation of displacement of the particle is y = (1m)sin(πt)