Question

write the equation for SHM( displacement vs time) if initially particle is at origin and moving in negative direction with respect to mean position. At A=2,and and T=4sec. A is amplitude​

Answer 1

Answer:

2sin( πt/2 ± π )

Explanation:

HERE'S THE SOLUTION

Answer 2

Answer:

This is the equation for the displacement of the particle at time t in SHM, given that the particle is initially at the origin and moving in the negative direction with respect to the mean position.

Explanation:

The equation for Simple Harmonic Motion (SHM) is given by:

x(t) = A*cos(ωt + φ)

where,

x(t) is the displacement of the particle at time t,

A is the amplitude of the motion,

ω is the angular frequency of the motion,

φ is the phase angle.

To determine the equation for SHM when the particle is initially at the origin and moving in the negative direction with respect to the mean position, we need to consider the initial conditions.

Given that the particle is initially at the origin and moving in the negative direction, we know that the phase angle φ is 180 degrees.

The amplitude A is given as 2, which means that the maximum displacement of the particle is 2 units from the mean position.

The period T is given as 4 seconds, which is the time taken for one complete oscillation.

We can use the relation between the period T and the angular frequency ω to find ω:

ω = 2π/T = 2π/4 = π/2

Substituting the values of A, φ, and ω in the equation for SHM, we get:

x(t) = 2cos(π/2t + π)

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