Question

The displacement of a particle varies according to the relation x=4(cost+sint). The amplitude of the particle is

Answer 1

Amplitude of the particle will be 4√2

Explanation :

The given equation can be written as ,

x = 4(cost+sint)

= 4√2(cost/√2  +  sint/√2)

= 4√2( cost sinπ/4  + sint cosπ/4)

= 4√2 sin ( t +π/4)

we know that the standard equation of displacement is,

x = A sin( π + ωt)

comparing both the equation we get,

A = 4√2

Hence amplitude of the particle will be 4√2

Answer 2

Given: The displacement of a particle varies according to the relation x=4(cost+sint). The amplitude of the particle is

So Displacement  y = 4(cosπt - sinπt)

                        y = 4cosπt + 4sinπt

Let Rcosω = 4..............(1)

     Rsinω = 4................(2)

 y = Rsinωcosπt + Rcosωsinπt

y = Rsin(πt + ω)

Squaring and adding (1) and (2) we get

 R = √4^2 + 4^2

R = 4√2 units  R is the amplitude.