​ A particle executes simple harmonic motion according to the equation x = 5sin(2 π/3 t) 1. find the period of the oscillation ​

Question

A particle executes simple harmonic motion according to the equation x = 5sin(\(\frac{2π}{3}\)t)

1. find the period of the oscillation

2. What is the minimum time required for the particle to move between two points 2.5cm on either side of the mean position?

Answer 1

1. x = 5 sin(\(\frac{2π}{3}\)t), when we compare this equation with standard S.H.M, x = a sin wt.

We get wt = \(\frac{2π}{3}\)t

2. y = a sin wt

2.5 = 5 sin w × t

Time taken to travel 2.5 from the mean position is 0.25 sec. Hence time taken to travel 2.5 cm on either side of the mean position is 0.5 sec.